1) Sounds like it might just be a question of cleaning it, which is pritty easy.
2) It's not that hard... sugest you solder 2 whires to it though and have the battery sepperat. a Cointype battery is the best option in my oppinion.
3) Secondhand computer market... SCSI drives drop every now and then. Get a 4GB one.
4) Only one ledft to upgrade with and thats 3.1. But you should uppgrade the CPU aswell... a 060 would be fine.

5) Get hold of an external SCSI CDRom. There's also software to connect up the Amiga to a PC through the Par port but that's SLOW.