You install it where it works. Sometimes you have to relocate something somewhere else to make room, like that pile of boxes on the floor next to the water heater.
If you're in Florida a 2" is probably fine you don't have to worry about the vent opening freezing over but you need to check the international residential code for where the vent is aloud to exit an exterior wall.
If the angle stop for the hot water line going to the sink has a valve stem with a rubber seat that may have come loose and is vibrating when the water is flowing.
There's more than one way to fix that. Go to a plumbing supply house, not Lowe's or home Depot and show them that picture. The person at the counter is usually a plumber. Do not use a fernco reducer, the rats will eat through it.
Push the pipe in until in bottoms out. Use a 4" fernco coupling. All sewage tanks use rubber couplings unless they have threaded outlets because they are made out polyethylene and you can't glue polyethylene.