Welcome to the world of Amiga.
Use the search function on this forum and I'm sure you will find the answers you need.
AFAIK the 37.299 kickstart only has problems with Harddrives and not the PCMCIA.
It does sound to me that the floppy drive is faulty.
The only problems you might have using EasyADF is, the amount of memory you have and the lack of a Harddrive to load/store the floppy image(s) to/from.
If it was my A600, I would.......
Upgrade the kickstart to 3.1.
Upgrade the memory from 1mb to 2mb.
Add a Harddrive.