Welcome to Pettalk .

We like to see photos on this site !!!

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As to your questions.....

Surely, it would be better if the four cats at your parents house stay together, as they would have bonded. Would your parents take care of these cats forever or do you have to rehome them.

If two of the strays are unfriendly, are you sure they aren't feral. If they are feral (alter them) but they'll want to stay outside. It would be best to have them altered asap, as you may never tame the unfriendly stray/feral cats.

Try shelters for cheap altering vets. Some shelters will pay for the vets, if you ask.

I leave the 'how many cats can fit into a house' question, to the inside cats only crew. Mine are inside/outside as I am in a quiet area of England.