Such as, can I vote in votes that were open at the time I took the oath of office?
I believe so.
What *exactly* are the rules on bill introduction etc?
Write a bill with suitably precise legal language, give it a name, and post it to the legislation introduction thread. That's pretty much all you have to do.
Gabu is essentially correct. I should add something, however.
Considering that your term only lasts for one week, if you write a bill that you wish to see voted on in front of the Senate, I would suggest to get someone else to co-sponsor it with you, so that person can reintroduce the legislation for next session.
You will lose your power to vote on it, but this guarantees the right to debate and eventual vote on the legislation.