#3 on your list is a definite safety hazard. Having the brakelights on whenever the headlights are on leaves the person behind you unable to tell when you actually DO apply the brakes. I suggest you consider this a safety hazard and do not procrastinate on getting it fixed. Note that it could be something as simple as a blown fuse or an incorrect or incorrectly seated bulb. Don’t delay.
As an aside, I’m shocked a dealer would or could sell you a vehicle with these symptoms. Don’t they do a safety check on used vehicles where you reside?
I would immediately return to the dealership (is it a Toyota dealer) and request that they repair the obvious safety hazards on the car they just sold you. I’d also tell them to take their time as you will be driving the free loaner they provide.