I'm thinking about dual booting my current ubuntu 12.04 OS with fedora 18. My question is when I shrink the current ubuntu partition, which takes the whole disk (with Gparted) will I be able to share the swap current swap partition with fedora? And will the swap partition move with ubuntu or will it stay at the far right side of the drive partition map (From Gparted's point of view)
Absolutely. Both Ubuntu and Fedora can share the same swap partition without any problems.
When your computer starts, you're given the choice to boot ONE operating system - Ubuntu or Fedora. That one OS you choose to boot will use the swap partition when necessary. The other OS can't use the swap space, as it hasn't booted yet.
To make Ubuntu and Fedora share a swap area, choose the existing swap partition as the mount point for Fedora's swap area when you install it, rather than creating an entirely new swap area.
When you shrink a partition other partitions are not affected.
Thus the swap partition can be shared with Fedora.
Infact, since only one operating system will be booted at a time, the swap partition can be shared among any number of operating systems.
The swap partition will remain intact as it has nothing to do with your Ubuntu partition.
After you shrink the Ubuntu Partition, you will get a Ubuntu Partition (with a smaller disk space) and some free space.