cant recall the ROM, I had downloaded it from one of the XDA links
Froyo
Kernel - 2.6.32.9
Baseband version: I5081DDJG6
Model# is GT-I5800 though it should have been I5801
That is the kernel version which is same for all.GT-I5800 is shown at boot or in system information thingy?If it is at boot you probably flashed a rom with bootloader from european version of the phone(I5800),if not nothing to worry about.
Just don't flash roms that have bootloaders because if any error occurs during flashing bootloader,you might brick your phone.ROMs from samfirmware have them.
With roms without bootloader the worst that could happen is a soft brick.
About the battery maybe your battery has reached it age.Try another rom,test and if battery is still bad,buy a new one.
Try kyrillos v9(v10 is 2.3),kyorarom ascedency,purumod etc for froyo roms.
Kernels available are g3mod,kyorakernel,astrum.