Why are you using such an old version of Slackware? It's now at version 10.2 and soon to release 11.0 If it's because you have an old computer, that's no reason to use an old version. Support and packages will be better in 10.2.
As for the USB drive, this is what I use:
/dev/sdc1 /mnt/usb vfat noauto,users,rw,umask=1000 0 0
/dev/sdd1 /mnt/usb1 vfat noauto,users,rw,umask=1000 0 0
They mount read-write (rw) for users, and if you use a desktop environment such as KDE, you can do this:
Click the System icon on the desktop, then click Storage Media, then click Removable Device (sdc1) or whichever is appropriate on your system -- which will open Konqueror as a file browser. After using the device, and before unplugging, navigate back in your directory to that system:/media/ directory and right-click on the device and choose Safely Remove.
NB: I have mine set as /dev/sdc1 and /dev/sdd1 because I have two SATA drives in this computer which are /dev/sda and /dev/sdb. You'll need to change those entries accordingly for your system; as well as make a mount point for the devices.
My mount points are under / and not /mnt because I like them that way, and these are perms:
mingdao@silas:~$ ls -alh /mnt/usb
drwxrwxrwx 2 mingdao users 1.0K 1970-01-01 07:00 ./
drwxr-xr-x 8 root root 192 2006-05-12 07:00 ../
I have absolutely no clue how mounting a USB drive would/could modify /etc/fstab. That's a new one on me.