Convert a device that is powered by a 12V 2 amp ac-to-dc SMPS to a battery powered device
Assuming you will still have automobiles in your off grid location; a very simple and cheap alternative is to buy one or two extra auto batteries. The car already has the voltage regulated charging system in place. And at a 2 amp draw, a typical car battery will run your device for quite awhile. 

Nevertheless, aside of offering an alternative, back to the question itself:

1 Yes it is possible. Even with building your own battery fed regulator, you have some options. You could make a battery pack that places several batteries in series til you have 3-5 volts above your rgulated output and use a cheap and simple linear regulator.
Or you could build a switch mode power supply as you mention. 

2 &amp; 3 
Pick a switch mode regulator chip and read its data sheet and app note.
Build the app note as a first step to gain experience building  a power supply.
Here is a youtube video that will walk you through using the MC34063.
The 34063 in boost mode will be easily able to handle your requirements and it has been used for some time in USB phone chargers and hubs, so there are a lot of schematics on the web easily found.
https://www.youtube.com/watch?v=qGp82xhybs4