I see you're using the online version. I myself use the CD version. But I can see from your screenshot, exactly why one may be confused between "rental expenses" and "assets". Looks to me like very poor web design.
Basically, (and I do mean "basically") assets are those things used on a recurring basis in the production of income. So the house is an asset. Installed a new roof on the house? That too is an asset. Replaced the old central A/C? That's an asset. Assets are not directly deductible per-se. Instead, they get depreciated over time. Assets are entered in the Assets/Depreciation section.
Rental expenses are those costs incurred on a recurring basis in the normal day-to-day operation of a business. For example, property taxes, mortgage interest, property insurance, electric bill, water bill, HOA dues, repairing that broken washing machine, etc. etc. etc.
Note there are situations where assets can be expensed. But in the interest of keeping it simple for now, I see no need to complicate things at this point. (Maybe later?)
Should I also calculate the expenses to only those days that the property was rented? Real estate taxes, Insurance premiums, Repairs, and Mortgage interest?
With the only exception being the property insurance, you don't need to calculate anything. The program takes care of it *if* you elect the option to have the program do it *for* *you*. The only thing the program splits between SCH A for the period of time it was personal use, and SCH E for the period of time it was classified as a rental, is mortgage interest and property taxes.
For property insurance, you will have to pro-rate that manually. Remember, a pro-rated amount of the property insurance is only deductible for the period of time it was classified as a rental. Property insurance for the period of time it was personal use is not (and never has been) deductible anywhere on your tax return.
For rental expenses (do not confuse this with property improvements) you only enter those expenses incurred will the property was classified as a rental. They do not get prorated. So things like utility costs and HOA fees incurred while it was personal use are just flat out not deductible anywhere on the tax return. You only claim what was incurred/paid from the date you converted it to a rental.
Again, please *do* *not* confuse this with property improvements which you enter the Assets/Depreciation section of the program. If you need more clarification I'll be happy to try. I'm just concerned that I might cause further confusion with what I call "information overload".
