What should we do to stray cats?

I'm facing a dilemma. There are 2 cats that often come nearby my house. One is the mother (who happened to come to my house even before I fed it) and the other a kitten that was born also nearby my house. I think the mother might have been abandoned by previous owner because she was comfy with humans. At first the mother was skinny and had infection. I helped her by feeding whenever she comes and buy medications from vets to treat her skin and cough. Now she's healthy. The kitten is also well fed because I helped it since it was a little. However because of my actions, both have a dependency towards me. Sometimes they ask for attention, which I give from time to time. On top of it, the mother cat keeps getting pregnant, which led to my neighbor who don't want their kids to play with kittens, throwing away the kittens. I think some of the kittens might have been dead too without me knowing it. I have very little control about this because the cats are always outside and anyone can do whatever they want. I don't bring them in or keeping them as a pet, because I don't think a Buddhist should keep pets. Which brings me to these questions: 1. Am I wrong for feeding these cats? my heart tells me to feed hungry animals if possible but of course not everyone sees strays as animals that need help. By feeding I also invite them to stay around my house (being more dependent on me and causing annoyance for the neighbor) 2. Am I wrong for thinking Buddhist aren't allowed to keep pets? 3. Since stray cats usually breed a lot. Should I neuter the mother cat? my hope is so that there will be no more kittens thrown away from their mother not long after birth, or to experience suffering. Is it wrong to neuter animals? Answers to these questions will help me decide on what to do next. Thank you. Namo Buddhaya.