It sure sounds like your floppy drive is broken. Maybe it just needs cleaning out.
It is correct that 4GB is the maximum hard drive size under 3.0 (actually you can plug in a bigger one as long as you only format the first 4GB as past that it wraps round and starts overwriting stuff). This is because of the 32-bit addressing.
You can't just install Simms on the A1200 motherboard but you can put a memory expansion card with up to 8MB in the trap door - if you want more then you'll have to get a turbocard.
There is info on hardware at
www.amiga-hardware.com, and AROS at
www.aros.org. I don't know about Linux as I never used it.