How to get LiPo battery protection circuit's function and schematic
Obviously, these specific batteries have no public schematics, because old-style companies, specially the Conrads of the world, don't generally publicise them. In the specific case of Conrad I can easily imagine it being from fear of people finding out the design quality before purchase. Or more likely because the Chinese guy they bought it off on a street corner doesn't do datasheets.

However, batteries like these are one in a billion and if something is widespread, the chips that make it possible are as well. Chips, as opposed to random LiPo's, often come with quite extensive datasheets with all kinds of examples.

Here's the first link I found, happens to be TI, could have been any number of different manufacturers.

Start by reading that, understanding that and trying a few others maybe and it is possible (though not guaranteed) you'll be able to look at a PCB inside a battery and determine which type of chip they used, from the components around them. Even if they are unknown controllers or their Asian knock-offs.

As for knowing if it's in there, I have always been in favour of a standard marking for that, identifying both situations, but if it's not a reliable brand and it doesn't say "Protected!!!" on the wrapper/in the datasheet, you simply don't know for sure without actually looking.

Side Note:
Be careful when looking, knicking/damaging a cell may be harmful to you, your equipment and/or surroundings in several ways.



EDIT:

When editing your post a tiny bit I noticed you specifically asked for singel celled protection, these are often simpler, so I quickly found a brother-device for single cells.



I'll also shortly explain in that specific case what they are normally for:


Preventing over-charging of the cell. Over charging a Lithium Ion cell often causes large amounts of heating and possibly fire.
Preventing under-voltage of the cell. When you take a Lithium Ion type battery below a certain voltage (the most well known types around 2.5V~2.7V) they break, so the protection turns them off around that voltage.
Preventing too large a current from flowing. Many battery types don't like currents that are too high for them. Lithium Ion batteries can provide a very large amount of current, even if they really don't want to. Because Lithium is a very reactive metal it'd be extra dangerous to over-heat a Lithium battery. So they add a bit of function that measures the current in and/or out of the cell and turn off the cell for a small amount of time (between a few and a few hundred miliseconds usually) if it goes much too high. It's a sort of a smart, self-resitting fuse.