Had to use T1 instead of T2 for the first two screws, think it might be all the accumulated grime and dust. The guide itself was very helpful and I managed to change the battery within 30 minutes even with those stupid clips giving me a hard time.

And because I read it in the comments above: I used a PH000 (1.5) screwdriver inside.

Regading the battery itself, I had to rebend the cable a bit and adjust the tape on the battery, because the position of the connector was off by about 3mm.