The missing player model shadows is another BF2 bug to my knowledge, I doubt we can fix this.
The crash/error you get when exiting is common, most of us have it. This is a BF2 bug, which happens more frequently in FH2 because the mod uses more memory. This is benign and you can ignore this one.
BF2 doesn't unload all memory between levels, so at some point BF2 engine may run out of memory. Restarting the game fixes this.
As said, FH2 uses more RAM than BF2 vanilla, so recommended is 2GB to 3GB RAM, and 256MB to 512MB video card memory. Updating your graphics drivers can solve instability, also ensure the GPU is cooled properly and power supply is sufficient.
Switching audio from hardware mode to software mode can improve performance, quality and fix instability.