Welcome! You are wise to join BYC and do lots of research before you make decisions. BYC members run the full range of chicken keeping from "pets" to "dinner". What we all share is a desire to do what's best for our flock. (Though opinions will differ.) Keep reading and asking questions and you'll learn who are the most experienced, practical folks are. (@aart, I'm looking at you!)
You’re in the right place for all your chicken questions. We all love questions! I don’t know about the pool. Cats though — cats are extremely variable. My family has had cats and chickens in the yards ranging together for generations. Most don't even look at each other. BUT there have been a couple who will look, chase or more — especially young chicks. Of course it can go both ways; we’ve had some cat-chasers too.
Eating your chickens is another thing altogether. Although I have a lot of experience there, I couldn’t advise you. It’s just too individual to each chicken keeper. Folks can tell you which birds to raise, when to process, how to do it, and give you good recipes. But the actual decision is too personal and no one can tell you what to do or judge your choice. If you do decide you want to go the full cycle from chick to table, we’re here to support you!
Welcome to BYC! It's very wise to do all the research as possible, first... especially planning the coop process even to the point of making sure the ground it leveled (that was one of my biggest mistakes).
I also have a pool but it really depends on what kind of yard you're working in. I live in the city limits with limited space in the backyard (including the pool) and after some lessons, I can only realistically keep 3 chickens at the most.
They've only fallen in the pool a few times by accident but, I've always been home so I haven't lost any but when I was a kid, 2 of my chicks died in the pool. The only issue I have is the amount of space they have. I would like to guard them off more because my dear husband gets tired of tiptoeing around poop when he just want to be in the backyard but, I know they're happy to free-range in what space they do have. So it really depends with the space and environment you're working with.
And with cats, it can go either way. I've spent the last 4 months "protecting" my chickens from the neighborhood cats, only to find out recently they're just curious and want nothing to do with them. ¯\_(ツ)_/¯
Doing your research and asking questions is going to help you in the long run. There are tons of information and knowledgeable peeps who are happy to help. Keep us posted and wishing you the best of luck!