Hi everyone! This is sooo soo random but I really don’t know what else to do!

Soo a week ago, a cat showed up to our house, and the cat would come and go, or so I would think, it would be here in the evenings and then come back the next evening

My boyfriend being the kind thing he is, started feeding it (of course the cat was going to return now)

Now fast forward to this week, the cat is just around the house all the time, it has a name already, (Monty) and we aren’t sure if it’s a male or female yet, it has a water bowl and food bowl and it likes to sleep under this thing we cover the grill with

The cat is absolutely so sweet, it likes to be under people’s feet and always comes out when I open the door to go inside and tries to come in

I honestly think the cat is a stray and maybe is lost and belongs to someone else because it’s so sweet and likes people

Im not sure what to do though and was wondering if people can help me answer the following:

•What type of breed of cat do you all think it is?

•Are vet check ups expensive just to see if the cat is okay and maybe has a chip?

•If we do keep it, sadly he’ll have to be outside most of the time because of my boyfriend’s allergies to practically everything, will the cat be okay outside?

•Any other advice you guys want to throw out there it would be very helpful, my boyfriend is 20 and Im 19 and

we have never had any pets or anything, please HELP!