That's a lot of stuff if you want a small footprint. Why not just get a Deco or Eero mesh router so you have routing and Wifi in one small footprint, and then get some Ring cameras and doorbell?
If you really insist on going Ubiquiti, why not the Dream Router which will also give you most of this in a single package?
Bad cable somewhere.
Do you own the neighborhood? Lol.
I don't know, but you can definitely enable 5G on your other AP. To limit interference, just set them to different channels. There are many more non-overlapping channels on 5G than 2.4G.
Not by a switch. You'd need a multi-WAN port router. Something like the ER605 will do failover.
You can add a switch, but you cannot splice.
You can use a Cat6 punch down junction box if you have to and can't run a new wire, but you are adding a point of failure. It should still work anyway, just keep the twists as tight as possible to the punch downs and mind the total distance of the Cat6 run from point to point. Another option is terminate it, plug it into a mini switch, and continue on from there to extend the distance and keep signal integrity.
Lazy electrician or cheap homeowner?
You got conned by marketing. First of all, you need a switch and not a splitter. Maybe it's just your terminology, so share what you bought and we can help. If it actually is a splitter, especially since you say it says Cat7, it has to be some POS junk that should be returned. As for Cat8 cables, anything you can buy on Amazon that is Cat7 or Cat8 is probably garbage. You should only ever use Cat6 at home. I would replace those as well and pick up a CableMatters or Monoprice Cat6 patch cable in whatever length you need. Stay away from flat cables as well.