Can the Jinn live with us in the same house? Can they posses us and do something to us to scare us? How can we protect ourselves from the Jinn? And did Imam Ali a.s really fought against the Jinn? And can we communicate with the Jinn?

Usually they live in deserted places. You can protect your self by reciting moawwazatain and ayatul kursi and hang dua Abu dajana on the walls of your home.
It’s true imam Ali (a.s) fought with the jins.