Hi.. sounds as if your back cover might be loose, in the back cover some antennas are included. If it's loose it would explain why the signal is weak and why the power button doesn't work properly.
Hi... I think, it is safe, the battery itself is in the soft part in the lower half of the assembly. If the film in he lower part is damaged or the battery is bend, then you should replace it. You should also replace the battery, if the capacity decreases, that could be a hint, that the film is broken and the battery is exposed to oxygen.
Hi did you try the OTA update or the update via SD card? No matter what, try the other way. Before updating, check the version, maybe the update doesn't start because the update is already installed....
