I built an Accessory Dwelling Unit on my primary residential property last year, and rented it out on Airbnb. The ADU is about 1/3 the total livable floor space on the property. Should I include 1/3 of the taxes and interest from the mortgage as expenses on the ADU?
Yes, you can do that. If your mortgage and taxes cover the two properties, you must prorate the expense.
Also, don't forget insurance. Homeowner's insurance is not a deductible expense on "personal use" property. However, if you have one policy that covers both your personal property and your ADU, you can claim the percentage of your insurance that cover's the ADU.
Generally though, I would expect you to have a physically separate insurance policy for the ADU. If so, then the entire cost of that policy is deductible.
The standard homeowner's insurance policy does not cover losses incurred with non-personal use. That's why I would expect you to have a separate policy for the ADU.
If the mortgage existed prior to construction of the ADU, you may only deduct the portion of the mortgage interest attributable to the land the ADU sits on. That is, since none of the borrowed money was used to built the ADU, you cannot use a building sq. ft. ratio