It would help to know how you house your chickens, what and how you feed them, etc. You obviously free range them if they are roosting on the pool gate, fence and yard lights, and the fact that they do roost in those places is not wierd at all, for a chicken. They will perch/roost anyplace they can reach. They will also fall in a pool and drown if there is nothing keeping them out.
Chickens like human company, especially if they associate you with food and treats, so for them to peck on the door for you to come out (not because they want to come in) is not weird either.
Chickens are pooping machines, so when you say they didn't used to poop that often, I'm wondering if you just didn't notice it as much as you do now? Maybe they are not pooping more, but it's just bigger poops because they are getting bigger. Do you close them up in a coop at night? Are you noticing more poop in there?
When you say they separate from each other, how do you mean? How many chickens do you have? It's not unusual for a flock of chickens to split up and go in different directions within their ranging area. Eventually they'll all come back together again to roost for the night.
Are you sure the chickens are eating so much more food or do you have rodents and or raccoons eating some of it? They are not old enough to lay at 3 months, they won't start laying until they are between 6 and 9 months.
So you see? You have perfectly normal chickens!!