Homeless cat - need your advice

For the last 1.5 weeks or so, a cat has been coming up to our house's back porch and standing there. She just watches us and she sleeps there too. A few days ago, we decided to give her something since she kept watching us eat, so we kept out water for her since i know milk can cause diarrhea. Then yesterday i was making a tuna sandwich so i gave her a bit. Now, she seems to permanently resid at our house. I put my guinea pig carrier outside and she sleeps in it. Whenever she sees one of us, shell come out and watch. When I go out to pet her, she is so friendly! She just rubs against us and crawls into our laps and purrs. She's very cute.

She doesnt have a collar, so I dont know what to do. Should I get her scanned for a microchip at the nearest vet? If so, how would i proceed.

I cant bring her in the house because the guinea pigs are in there, i have semi allergies to them, and my parents have pretty severe allergies. Not to mention, my mom can't stand cats.

Please....I have no idea how to proceed. Ive done lots of volunteer work at a cat shelter before, but i have no clue what to do here. My dad says that if we find out she doesnt belong to anyone, we can adopt her and make her an outdoor cat.