Think very carefully. Is this phone brand new? Or is it second hand/refurbished?

If it is brand new, never touched by another person it sounds like the battery is fuc***. Perhaps too old and stored in noin ideal conditions (possible if it has been on the shelf since 2009).

If it is second hand/refurbished, again battery also do a COMPLETE reflash. rootFS and eMMC.

The FM transmitter is known to be a bit wimpy (for legal purposes) however there is a program in the application manager called FM booster that increases it's power. It helps ALOT.

Also ONLY use application manager over wifi...