Hi there Oscan Sammut,
Do you get some kind of error when trying to install the game on F:?
Regarding your C: drive losing space, I would say that your system is most probably creating restore points. You need to adjust your System Restore settings(reduce the HDD space allocated for that) and delete previous restore points.
See how to do that: http://www.howtogeek.com/howto/5482/make-system-restore-use-less-space-in-windows-7/
Some more ways to free up HDD space: http://www.howtogeek.com/125923/7-ways-to-free-up-hard-disk-space-on-windows/
Hope this will help,
D_Know_WD