How to patch drywall when the surrounding wall is rough/bumpy?

[Flyover]

The walls in my garage are bumpy, almost like popcorn ceiling, but are drywall nonetheless and there are several holes in them. We have mice in the attic above the garage, so I figure it makes no sense to try and take care of the mice when they still have all these "doors" to get into the attic. (At the same time I feel like this is pointless and they'll find a way in regardless.)

In any case I figure it's a good idea to repair the holes the previous owners so graciously left me, to restore at least some order to the universe. But how do I patch the holes when the surrounding surface is rough and bumpy like that? I don't really care about matching it, but I'm concerned about how to properly apply drywall tape/putty in this situation

Sorry about the bad picture quality...blame the flip phone. Just enough to give you an idea of how the wall looks:

 

[Snoonyb]

In #1 & 2, I'd remove the material to the center of the studs, on both sides, and square it up and secure the replacement.

For #3 I'd place a piece of mesh tape, inside.

For #4 I'd cut some drywall 3" wider and longer than the damage, remove the damaged part and on the reuse side of the patch piece, in the center, cut the shape of the patch, being careful not to cut through to the finish side of the patch material, then every few inches strike a line from the cut, out to the edge of the patch material, bend the material away from the patch cut and peel the gypsm off of the finish paper, fit and adjust.

This is called a butterfly patch.

I'd use a setting compound, for all four, and mesh tape on 1,2 & 3. For #4 I'd butter up both the edges of the holeand the patch, and the paper mating surface around the hole.

I'd use 20min. or durabond.

 

[Flyover]

@Snoonyb, for all 4 of them why not just cut a large rectangle around the damaged portions and then fit the same size rectangle patches back in?

In general the main thing I'm wondering is whether the rough surface of the wall will cause problems when trying to use conventional drywall patching techniques.

 

[Snoonyb]

I suggested those methods, to broaden your horizon/s, however, you can do whatever you feel best fits your skill level.

You said you weren't interested in matching the texture, so just either mud over, our scrape it off.

It's not, at all likely, that mice enter a wall cavity's stud bay, transverse up to the double top plates, gnaw through and into the attic.

 

[Flyover]

Thanks as always, Snoony.