The a/c fan should still be comming on. Your statement of car dosen't know the a/c is on sounds TRUE. On my focus if the selector is in certain positions it won't let my ac run. Bypassing it and manually changing doors might have something to do with this.
need to check for signal at he relay. You can jump the compressor to test the clutch activation
You can use a 90degree pick or screwdriver to pry relay from underneath to check for power or swap in a known good relay
Blower hitting probally bad blower mabey bad cage also, Turning off probally resister/melted resister plug end or just a dead fan motor need to check power and ground at fan when it's not running. I would fix this Piece by piece. And need to take freon pressure should be around 45lbs at low side.
Rims, fog light conversion, Interrior lighting recolor from starfuryt