Updated day 13..
I really thought ammonia would have zero'd by now
Grr!.. more waiting i s'pose hehe
1) My API kit detects 0.25ppm ammonia in my tap water. Should I expect my ammonia to just get to 0.25ppm, or should it go to 0 now?
It should go to zero.
2) My nitrites are higher than the API kit measures (BRIGHT purple).. is this okay, or should i do a water change to get them within a readable level?
The cycling advice you'll find in the advice section will just say let it run (i.e. let the nitrites build to stupidly high levels). I don't agree and would advise you to do a water change to reduce the nitrites to a measurable level (i.e. less than 5ppm at all times). You may need to do a 90% or more water change to achieve this though.