Welcome to the GParted forum.
Some answers:
1. GParted is a software (source code) that one can compile and install in any Linux system. Various Linux distributions provide compiled versions, ready to install. The GParted livecd is an ISO file to make a cd. This cd can boot the computer and run GParted in RAM only, without the need to install anything on the computer.
2. GParted doesn't run under windows, it needs Linux. So, you have to boot from the livecd.
3. Formatting a partition doesn't necessarily erase the entire content of that partition. However, some parts are overwritten to create "entry points" to the new file system. This means that there is hope to recover the data, at least partially. You could try to use the "testdisk" software, that is able to scan the disk surface to detect any possible partition start point. Testdisk comes on a live cd together with "photorec", another recovery tool that is designed to scan the disk for specific file types. The GParted livecd contains testdisk (it works from the terminal window), but not photorec.
GParted is a powerful tool, used by many system administrators on professional systems and servers. We always advice to read the GParted manual in the documentation page, before any modifying operation. These operations are potentially dangerous for the data safety in case of error or any hardware failure, so backup of any important files is recommended.
(Topic moved to the live media section)
*** It is highly recommended to backup any important files before doing resize/move operations. ***