How can I fix carpet?

When our dog was a puppy, she went through this phase where she tore up the carpet. There's a hole in one spot. It's a 5x5 inch patch that is missing. There is a couple spots up against the walls/doorways where the carpet was peeled back and occasionally gets kicked up (drives me crazy!). There is another spot where it's like a run in the carpet (kind of like a run you get in pantyhose).

I live in an apartment and we will be living here probably for at least another couple years, so I would like to fix it up somehow. Just a temporary fix, good enough to where it doesn't keep getting peeled up.

I'm not concerned about not getting our deposit back. They were putting nicer new carpet in the apartments, but never got the chance to put it in ours before we moved in. So they will be ripping it all up and replacing it when we move out anyways.

Due to where the spots are, covering them with rugs, furniture, and other items won't really work.

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*edit*

I clearly stated in my post that a rug will not work for these areas 🤦‍♀️