You should be fine copying text files from windows to linux. I do it between partitions all the time. As far as the floppy drive, you can do a
mount /dev/fd0 /mnt/floppy
from a bash prompt as root and that will mount all the info on the floppy into the /mnt/floppy directory (which must already be created). You can also add this to your /etc/fstab but since I'm not sitting in front of a Linux PC I won't even try to get the syntax right on that...
Hope this helps a little