In the VPS, when I use it to surf, will the resolution of screen that sites track be the same of my pc or can it be modified by the software that I use to log in?
This soely depends on the browser you use. If you use something like the TBB on your VPS, resolution based tracking should be rather hard. Please keep in mind though that the provider may track you and furthremore, that this is not really a question which fits in this forum.
Have a nice day,
Keystroke and mice fingerprinting also applies, see: