My '02 SR5 Sport locks and unlocks with the ignition, also. I think its a setting on the factory alarm system. It also hi-lo beeps at me after a set amount of seconds of being off which is notification of it auto turning on the alarm. Like I cant reach through the rear window and unlock my drivers door lock without the alarm going off. I don't even have a key fob for my alarm :/
My headlights turn off when I open the DRIVERS side door only, with ignition off. I think that would change, however if I ever get around to disabling the DRLs...?