I put an outdoor, waterproof fan on my rabbits all summer. I live in FL in the US and it gets hot here, too. I also freeze ice blocks in old sour cream containers or things like that and put them out there, though if yours don't have a raised hutch system like mine it might get messy. I know people will freeze water bottles or soda bottles and put them out there, too. That might be less messy for something on the ground. Every once and a while I'll throw some ice cubes in their water bowl and bottle but it probably goes warm before they even drink it so I haven't done that too often this summer.
The last thing I can think of is to keep them well groomed, to keep any excess hair out of their coats that might make them hotter.
As for the mice, I'd suggest traps and maybe putting wiring or something else to cover them so your other animals can't get in but the mice/rats can. We set up just simple plastic snap traps that work well and bait them with peanut butter usually and cover them with wire or we actually have an old laundry hamper we use lol. I don't know if mice are different on baiting tactics though.
