@Debi5 Oh! So many questions!
1. Taxes: In some areas, like San Francisco, Florida, and others, Airbnb collects and pays the Occupancy tax on behalf of the hosts. In other areas, like where I live, I need to collect and pay myself which is a bummer. Here's what Airbnb says:
https://www.airbnb.com/help/article/653/in-what-areas-is-occupancy-tax-collection-and-remittance-by-...
https://www.airbnb.com/help/article/654/what-is-occupancy-tax--do-i-need-to-collect-or-pay-it
I chose the option to just include it in my nightly price to avoid the hassle with the guest.
2. Pet Fees: If you receive a reservation inquiry, you can send the guest a Special Offer to include a pet fee. If you receive a reservation request, you should discuss the pet fee and get agreement with the guest that they are willing to pay extra. If so, accept the reservation request then go to the Resolution Center to request payment for "Additional Services". Here's the link to the Resolution Center:
https://community.airbnb.com/t5/Hosts/The-Resolution-Center-A-Community-Help-Guide-Request-or-Offer/...
3. Damage Deposit / Damage Insurance: First, you need to set a Security Deposit on your listing so guests know that you may claim it in the event they damage something. Here's the help article on Security Deposits:
https://www.airbnb.com/help/article/140/how-does-airbnb-handle-security-deposits
You make a claim on the Security Deposit through the Resolution Center.
As to insurance, all hosts should have their own insurance to protect the guests and themselves. In the US it is hard to find companies that insure vacation rentals. I did through Farmers Insurance who was able to get Foremost to underwrite the policy. I also hear AllState is offering it, but not in California. Talk to your insurance broker.
Since you are new, here' a link to a Community Help Guide with links to many commonly asked questions. You should bookmark the page for future use.
Hope this helps!!