Is there an offline airplane route software similar to the in-flight entertaiment map?
1) The software from various airline companies seems to be more or
  less of a standard. So they should work in a similar fashion. Which
  input is needed in order to make it work (i.e., altitude, lat/lon
  coordinates, temperature)?


"Inputs" from the aircraft devices, like pitot, anemometer, gyro, etc. ? I don't know. DeltaLima answered that for you. What you see on the screen is definately a software rendering, that means an operating system is running, and displays a frame on that screen device. The graphic is software-generated (the map, the plane, its orientation, the text, the sun, the clouds, zooming, etc.)

So, at some point, the inputs signals (altitude, cruise, heading...) has to be converted in computer bytes that will be handled by hardware devices of a computer, buffered in memory, then used by "some software" in the way they have been designed for.

Option 1 :

There's a central Operating System (OS) that holds all the computable datas and feeds all onboard software on demand including FMS, IFE, etc.

analogic device -&gt; convert to computable data (bytes) -&gt; central OS
                                                        / | \
                                                      /   |   \
                                                    /     |     \
                                    Cockpit softwares    IFE    Cabin Softwares


Option 2 :

There's no central OS, but multiples ones, and a direct star-type (tree) data pipeline.

analogic device
 |_ convert to computable data (bytes)
     |_ some software on some OS
     |_ some software on some OS
     |_ IFE softwares on IFE OS
     |_ some software on some OS


Option 3 :

IFE Software is a included in one OS that also run other softwares

analogic device
 |_ convert to computable data (bytes)
     |_ OS1 (cabin)
     |   |_ IFE softwares
     |   |_ Inflight intercom software
     |_ OS2 (cockpit)
     |   |_ Front Panel softwares
     |   |_ BlackBoxes softwares
     |_ HUD software (of packed software in hardware)
      ...
      ...


There are other Options, each one could be better called "onboard System"

By the way, if, by "inputs", you meant "how to make that tiny plane move along the map", there are thousands of ways doing it, but the schemas is the same :


draw a map (use some gree/blue/brown color to make it look good enough)
draw a path using points locations on a X-Y (invisible) grid and line segments
slam a top view of a plane on all of that at a precise X-Y location (and don't forget to rotate the plane icon in the correct heading or your passengers will start to panick)


No matter how beautiful the flightpath could be rendered, remember it's a computer generated graphic, and doesn't need to be accurate at all. For example, refreshing could be set at an interval of 5 seconds instead of real time (5 seconds is good enough even for steep turns on final) The map resolution doesn't require a milimetric precision. 1000ft or 500ft lateral precision could suffice, and even if the displayed (text) altitude is in feet, the 3D rendering doesn't care about that at all : it uses a fraction of that altitude, then accordinly shifts the position of the aircraft model on the screen to give you the impression the aircraft is at an higher altitude...

That the logical way the flightpath software requires. Accuracy and physics computations are not required, unless you want to create a game or even better, a simulator (in terms of reproducing nearly-real behaviour in a virtual world) GoogleEart's Flight game for example isn't as precise as many other games out there (Lock On, X-Plane...)

But for all of those, the "inputs" are all binary datas stored in memory and used as variables by the software. Turning a plane isn't dependent on a heading value. It's one block of the software code that reads the heading variable, then rotate the object (the plane) by the corresponding angular value, then another block of the software code draws (renders) the object on a screen buffer. Finally, the screen buffer is passed to the displaying device (your IFE screen) and each pixel of that screen shows what has been calculated by the software for the human eyes.

In the end, what you see on a screen - ANY screen wether it's your TV, the IFE, your computer screen when you read this answer, your phone screen - is a series of slideshows pictures rendered by the screen device one image after another. But it's done so fast that the human eyes (or brain actually) think what is shown is really moving. It's not, but looks like.




  2) Is it possible to acquire one version of this software and run it
  offline as a simulation, giving as input the needed information?


I tend to say yes ! but wait !

Good luck finding that software though. You should ask someone working for an IFE system provider for aircraft manufacturer.

And note one thing : Such softwares could be packed in some hardware components having an inbuilt memory card, this preventing anyone from copying that very software while it is successfully loaded in the IFE OS just like any other software loaded from disk/CDs/USBs... Of course you can't unplug the hardware device from the IFE hardware motherboard, and plug it on your computer motherbord, that wont make it.. Just like your phone (wether android or iphone or whatever) the firmware is burried deep in one hardware component. You can't easily copy a firmware from an iphone to a nexus.. :P 

But at one point, those softwares has to be created on a computer, then, have their "saved as files" state in the computers of the enterprises creating them.

As you could have guessed, chances to get a copy of such software is pretty.. non existent, not because it's nearly impossible, but because such software are copyrighted, and/or the (hardware) system supposed to work with aswell. A flightpath IFE software developped by a company may fail to work on your computer if you don't have the same OS architecture as the company's, and/or even some hardware devices that may be required to input or output valid binary datas read/written by the software.

Someone who has a copy of such software wont tell you he has...

I can tell you the Air Austral IFE is Linux based Operating System. The flightpath map displayed, the movies/music/games entertainments are all running on that OS. While the IFE on some Air Madagascar planes could be Linux based aswell, the softwares (the rendering and graphic layout) are different, meaning that those are not the same softwares as the Air Austral ones (or other versions)




  3) Is there a freeware solution to this? I'm more interested on
  information like the geography, cities, countries and borders.


An authentic flightpath software like those onboard aircraft ? Nope ! Never seen one in the items library of a store, and never found a page using google of a page "FlightPath Software Download".

A software that shows earth, oceans/lakes, country boundaries maybe ? Yes !


GoogleEarth/GoogleMaps
Nasa Worldwind
Bing Maps
Many little and less widely used software on SourceForge using rendering libraries and web hosted databases
...


A software that allows you to draw/show paths (and objects if possible)


GoogleEarth
Cesium
Nasa WorldWind
Marble
...


A standalone software that shows you (simulated) realtime flight of an aircraft over a map or 3D Earth ?

Anyone who tried creating such software ended making it a web-based application that you can access only through a navigator (like FlightRadar) Otherwise, it would be the decision of an enterprise or organism to hire developpers to produce such software for internal business purposes ONLY !


display aircraft on a radar screen
display meteorogical objects evolution on a map
display satellites movements at a space center on a large screen
(^^ purposes like that that has nothing to do in public domain)


That's exactly what IFE hardwares/softwares is about : have a bunch of engineers/programmers, build the devices/softwares, sell them to airlines/aircraft manufacturers. Panasonic, Thales, LiveTV of JetBlue, Rockwell Collins... Don't expect them to upload their baby on a website and allow you to download them..



So far, I said "anyone who tried..." ... ... failed ! Because building such software, to be accurate enough and interresting for you and me, would require a massive amount of datas :


flightpaths are not straight lines from airport to airport. You can spot this with FlightRadar, then you'll need each airport data, with their SID/STARS; you'll need waypoints, you'll need routes (those you can see on a real jepessen map) etc.
of course, you'll have to maintain those datas up to date.
those datas are NOT freely available, so if you're a developper that paid acquiring them (or a company that employs developpers) you should find a way to make profit on it. That's what Microsoft made with Flight Simulator, what Lockheed Martin is doing with Prepar3d, X-Plane, etc. Games are selling well, but a simple "show my flight plan" software isn't interresting enough to make profit on it. For you or me perhaps, but not at all for average people.
And because the datas has to be updated, a standalone application that doesn't connect to the web would prove impossible to achieve, as it will be obsolete soon enough and would require anyway an internet connexion and mostly a registering (payware) for stream updates. Most applications that does this are web-based applications, not downloadable ! This is even more not standalone if you are thinking of displaying an actual, flying, aircraft (like FlightRadar) - And you'll have to purchase access rights on some radar centers... and implement the programatic logic to handle those streams of datas at runtime.
What about maps ? If the plane is flying above the city of New-York, what are you going to display ? A greenish-brown landscate ? A text showing "New-York" ? What about the shores (or how the software knows there is nearby ocean and land ?) Yes, you must have a landclass/waterclass database. The way the datas are stored highly depends on the way the software displays them. You need raster (images) tiles of the earth if you want photoreal-like terrain, or vector-based datas for computer generated landscapes. The later is lighter in terms of required disk space, but vector-based datas ar good for flat terrains (projections) To have datas for mountains, valleys, etc. you'll need anyway discrete values of land elevation around the globe. The disk space used quickly rockets... So don't expect from someone the task to compile all those datas for you.. and there are awfull voids here and there (in far far away land on this earth) that you can't retrieve freely on the web (well, there are 100 meter resolution terrain elevations available for free out there, but higher resolutions are very hard to get for the entire planet)
That's why on flightplans IFE, you can't zoom in and see roads on the map ;) 




I've started developping my own "show aircraft routes and display realtime flying tiny aircraft over a map" years ago, still, it's stucked as a "Work In Progress" due to the massive amount of new issues occuring and the interlacing complex features I would like it to have (Compatible with the game simulators mentionned above)

There's almost one new created airline every week, one new aircraft delivered every day, updating the - offline - database of that program occurs on a daily basis, weekly at longest, and I still need internet for that ! So, the day I may release that application would never come before I die. Just to pick an example, the application is developped as a Windows Forms interface. There's a better interface provided by the dotNet Framework called WPF. Upgrading the application to this new architecture would be a must before releasing it, and I have no time to do that. The database weight several Gigabytes (as expected : Maps and graphics...)