Ear mites are tenacious little boogers. You could bring them home to the cats (humans can be carriers for ear mites) from anywhere. They could also have something else, like an infection, but I'm willing to bet since they both have it, and it is only in the ears (right?) that its ear mites. It needs to be treated by a vet. DO NOT give any over-the-counter medications for ear mites, fleas, worms, etc to your cats. But a vet can clear it up with inexpensive, easy medications and a cleaning.
Vaccinations, well. If you do a search of this subforum, you will find several threads about just that-- indoor cats and vaccines. In most places a rabies vaccine is required by law, so you must get one. Other diseases are very easily spread, and you're better safe than sorry. And on top of that, bad things happen, such as an escape, a stray finding his way in, a disaster, etc. Some vaccines, on the other hand, you're probably better off without.