@Matthias_BL
Big cheers for effort to show the whole process!
Great work, really, you showed in detail the process of opening of device with available tools to help in this situation. Back cover is very flexible ant it will not brake, just small plastic notches are somewhat fragile. These small plastics notches will not brake also, just if they are opened and device is assembled like this multiple times, they will wear out...
1) Any electronic components store (which sells resistors, capacitors, transistors, SMD components and similar) will have this LiPo batteries. I live in a rather small town in Serbia and have several stores like this in my home town.
I bought just some random LiPo battery (made in China of course
)with maximum capacity I could find in dimensiones which will easilly fit into device (1100 mAh, 3.7 Volts, 50x60x3.8 mm) It costed me around 8 euros. If cannot find thinner battery, I think around 6 mm thickness is absolute maximum, above that back cover is problem to close fully.
2) Removing of old battery is really a problem. Battery, like you noticed, is glued with some kind of extra strong but flexible glue.
You must be very patient and work very slowly. Reduce bending of screen also, try to avoid it completely.
You will not brake back of screen, just go one step at a time.
I must mention this: deformation of old battery during removal is unavoidable, but caution must be applied. Perforation or significant deformation of LiPo battery is great fire hazard, BE VERY CAREFUL. I think the safest way to remove battery is some kind of hard plastic card or similar object. Put it under battery and push slowly until glue is removed piece by piece. I used this method.
3) Capacity of battery is absolutely irrelevant from device standpoint, just find a largest capacity within dimensiones of space for it. I considered putting a mega battery (like 4000 mah, but device cover must be designed by you and correctly assembled). I am thinking about ways to implement this