1) First, create the /mnt/sdax directory. Mount your new partition there. From the command line as root:
mount -t ext3 /dev/sdax /mnt/sdax
Move all the files within /usr to /mnt/sdax. Now everything will be on the new partition, and you just need to tell the system where to find it. You will need to edit the /etc/fstab file. I recommend as root:
You will need to add a line as follows:
/dev/sdax /usr ext3 [options] 0 2
(I'm not too familiar with the options for ext3, but just use the same options as the / line)
Don't forget to save out of nano, use control-o.
You'll need to reboot your machine, but you should be all set.
(after you reboot and everything is properly showing up under /usr again, you can delete the /mnt/sdax directory)
2) For your partitioning/formatting needs I recommend using gparted. You can install it as part of your distro, or you can download and burn a live CD (which is what I really recommend)
3) Sorry, I have never installed slackware, so I can't help you with this one...
I hope this helps, and good luck!