okay so it does seem as if she is in a play bow and wants attention. my guess is that she never learned bite inhibition so she doesn't know to control her mouth. you need to teach her that she can control how hard she bites. when she bites inappropriately -- immediately withdraw all attention for 5 minutes. don't look at or speak to her. just get up and leave. she will learn play too hard = no more play. you have to do it everytime tho and your parents too.

for the stairs i suggest you teach her to wait. wait until you are up or down and then you give a command like up or down or whatever will mean okay you may come up/down stairs now.