Dome lites wont shut off

I just bought a 2005 cadilac srx v8 80,000 miles took it on a 400 mile trip the
day I bought it,it ran perfect until the end of the trip when I exited the freeway
into stop and go trafic I got a transmision hot engine idle code ,pulled over
and shut down for 10 minutes and code cleared, next day started cold
noticed starter dragging but started,drove short distance and got transmision
hot code again,shut down 10min code gone again,the engine hadn't even
warmed up yet and no noticeable  transmision problems,became suspicious
of battery being week so bought new battery and no more transmision codes
but now the alarm goes off for no reason,interior lights wont shut off,doors
wont stay locked and get a rear lift hatch adjar code,driving me nuts,any
ideas