Feral Kitten-Need Advice

Hello everyone, as the title implies I am needing some advice on a feral kitten we have been feeding in our backyard the past couple of days. I apologize I hardly ever use this app so I'm not sure if i'm in the right place.

The past few days there has been what looks to be maybe 7+ weeks or so kitten regularly coming to our yard to eat some food that we've left it. I've been watching like a hawk to see if there are any siblings or even a mother nearby to no success.

I would really love to adopt this kitten but am at somewhat of a loss on how to go about doing it. I've purchased a trap and am going to get my hands on some pee pads but I have no idea where else to go from there. Thankfully the weather is still warm where I live, but if I were to successfully catch this kitten, would it be ok staying in a trap overnight outside with some food and water? I will cover the cage with a towel of course. I should mention that this cat only stops by our house at 8~9 pm. I have not been able to get the kitten to come sooner. I will look to call the vet ASAP regarding how to proceed with testing+neutering but frankly I dont even know what to expect in that regard either.

Ideally i know its best to bring a kitten inside where its sheltered but I cannot risk my two existing cats to catch any illness the kitten may have.

TLDR; Stray kitten (7 weeks?) in our yard that only comes at night, no family sighted, have a trap ready but dont know what to do afterwards, dont know what to expect at vet either.

I sincerely hope this doesnt come across as someone making a rash decision. I have been worrying about this cat day and night trying to figure out whats best to handle it...any and all help is certainly appreciated!!!!