I just removed the old battery parts by gently leveraging them with a wide wood chisel (like a very wide screwdriver). The glue stripes were not that tight and everything worked well. There’s no need to disassemble the Mac in lots of steps and risk to damage something by mistake.

I always use a bottle of wine and a rubber band to fix the upper part with the screen while working on the bottom part. Removing all connectors could result in connection problems so I avoid this by all means (ruined an iPhone 5s this way).

I also discovered that I didn’t needed to take off the screen protector. It fit that hard to the screen that the removal tool didn’t even cause the slightest bubbles.

Wenn der Home Button nach dem Austausch immer noch nicht funktioniert, sollte man sich die beiden kleinen Kontakte anschauen, die auf der Platine an einem Flachbandkabel sind und auf die in dieser Anleitung zu sehenden messingfarbenen Kontakte drücken. Ist einer dieser beiden Kontakte defekt, muss man den Lightning Anschluss ersetzen. Kostet zwar unter 5€, ist aber ziemlich aufwändig, da der Akku ausgebaut werden muss.

Yes, you have to remove the piece of paper or plastic to install the new cable.

Bei mir ist das Federkontaktkabel des Home Buttons defekt. Welches Ersatzteil ist dies und wie tausche ich es aus?

Delivery and replacement were fast and easy. After booting up I checked the new battery with Coconut Battery and found the load cycles at 1 which was what I expected. The age of the battery was indicated as 37 months old and thus older than my MacBook Air. That's not what I expected.

Don't batteries get old from just lying around?

Is there any way to exchange the installed AirPort/Bluetooth Card with a newer one providing W-LAN AC?

The replacement cable comes without the sleep led attached. Thus you have to remove the flat cable of the sleep led from the socket of the old hd cable. Take your fingernail and lift the side of the socket opposite to the cable. It's really tiny! Afterwards insert the new cable and push gently on the part lifted up before.