97 corolla problems

hey folks, thanks in advance for any insight:

1) i recently started driving my wife's old corolla (85k) until i get a new car in the spring. the first thing i noticed is that the shifting of the automatic seems off - as in it stays in second far too long before shifting into third. it's kind of like driving with the overdrive off. is this a timing belt issue? i'm pretty sure this car had its trans fluid changed at 65k or so. another possibly related symptom is that i noticed what feels like coasting or power loss once in a while under normal conditions. to me, this would seem to indicate gaps in the trans teeth. any ideas out there? i hope to sell the car soon, but who knows. it would suck if the trans is going bad this early.

2) i've recently noticed this weird power/wiring thing where if i press on the brake pedal when the car is parked (no key required), the dash lights up and the buzzer comes on. in most cars i've had, only the brake lights come on. any ideas? tx so much oh gurus of all things toyota!~