Josh, I'm late responding, but I think I can help with this. Here are some tips I've (finally) learned:
For "other deductions", put in any cleaning fees you are charging. Not things you buy. You can deduct those on your income tax return when you put in your earnings for airbnb, not here. I think it's important to deduct this here because the cleaning fee will be included in any tax reporting that airbnb does as part of the money you've collected, and may suggest to the City that this is the base price you received, when you actually collected that to pay folks who clean your space.
This is a tax on lodgers, not income tax. That means the lodgers are supposed to pay and we end up (unfortunately) having to collect. So it's a mistake (that I made at first) to see it as income tax. You can't deduct your expenses here. Save those for state and federal taxes later.
Here's another very important point: if you just add the amount you are collecting to your base price, you will be taxed on the tax! So you can't just figure out what 10.75% of your base price is. You'll end up paying 10.75% of that 10.75%! (My husband does this calculation for me, and has an algebraic formula that I could forward if anyone is interested. It's simple, apparently, but I'm no good at that computation personally. Sad.)
This year, I'm collecting the tax separately. It's a pain, but no guests have complained yet. This is what I do:
1) I make sure I notify them in my listing that I will be collecting it. (of course, no one reads the whole listing, but it needs to be there.)
2) After they reserve, I send a "check-in information" message and tell them again, this time calculating how much they owe, explaining that this is the City tax, not the state tax they've already paid, and apologizing for the inconvenience.
3) Before they leave, I send them ANOTHER message, saying: "Hey, before I forget, how would you like to pay your $______ Lodger's tax? We can do Paypal, Venmo, the Square, cash, or use Airbnb's Resolution Center. What do you prefer?"
So far, only one person has stiffed me. Everyone else paid up graciously.