Got the new tire this morning, then took it over to a shop to have them check out the brakes. They did a very thorough job (took about 45 minutes) and couldn't find a thing wrong. They also checked out all the joints / suspension / etc and said everything was really tight.
Said the pulse (he felt it too on his test drive) was so little that it wouldn't be worth it to do rotors right now.
The battery light came on while he test drove so he checked the voltage (without knowing I had already had that looked at) and said the same thing. Weak battery, altrenator is fine. I will be doing that and getting a new horn and new door pinswitch tonight.