>so I can just take some mesh and staple it to the hive? over the entrance.
If it's big enough for the bees and the drones to get out and small enough to keep the mice out. I've used 1/4" but some say that's too small. They sell mouse guards at the supply places, but I've not used them.
>And for a top entrance, can I just drill a couple holes in the top of the hive?
I hate holes in my hives. I'd cut a notch in the inner cover if it doesn't already have one.
> or does it require something more in depth than that?
The hole will do. I'd just prefer not to have the hole. Another option is a Imirie shim.