Hi BlackBeauty, and Welcome to TSF!
In answer to your queries.....
1. Some of these utils require running from a floppy - I don't have a floppy drive. Is it sufficient running it from the hard drive or perhaps from a USB memory stick?
Yes you can, but you will have to alter the BIOS to boot from a USB device, or better still put it on to a CD and boot it from there.
2. For the memtest86 tests, how do I run the tests on each stick of RAM? Take out 1 stick and run the test, then replace and take out the other stick and re-run the test?
One stick at a time; then, with both sticks. This means that you will be running the test 3 times in all.
3. Is the computer able to be used during these 8-24 hour test periods? What if the PC hangs during the test (it sometimes hangs from just moving the mouse)
No. This is because the Memtest operates in DOS(prior to Windows® booting), and you don't have the mouse in operation, just the keyboard. The chances of the computer 'hanging' during the test would indicate that there are other problems, usually with the RAM.
Hopefully this answers your questions. 