Cat questions: Microchip or not? Vaccinate?

So, we’re moving soon and I’m a little worried about how one of our cats will react.
He does very poorly with change. We already brought him to the new place, and he pooped on me, and in front of everyone. He tends to poop in front of people when angry about something, or when things change. (he did this when we lived someone else, and got made at us for moving…we had him neutered and he behaved after that.)
He also loves to try to run away, and since we live in a duplex, when he runs outside our door, he just goes into the hallway of the house. He likes to be outside, so I take him out on a leash so he can rub around in the grass.
We’re worried he’s going to run away at the new home. Or, could he be trying to escape because we live in a relatively small apartment and he wants more room to run around and explore? He usually runs out of our apartment towards the basement to sniff around. When we move, he’ll have a very large house to be in.
Should be get him microchipped? Is it safe? Are there any complications?

Also, our cats have not gotten their vaccines for at least a year. We’re currently looking for a low cost place to go, since our vet is pretty expensive. But, will our cats be okay if we move in with a dog that is vaccinated? (I know nothing about anything that can be transmitted between species)
btw, the cat in question is turning 3 soon, if that means anything!