How can I fill these holes?
If this is drywall I would buy a small bucket of plaster and some drywall tape (the mesh kind), drywall knives and patch the smaller once that way. The bigger one I would cut a bigger square hole from stud to stud and cut a nicely fitting drywall piece to fit into the square. Fix it to the studs with drywall screws. Then use the same drywall compound and drywall tape to patch up the seems of the patch. All the stuff should be easy to get in the store. It takes some skills to get all of that smooth. Check out some drywall videos on youtube