@bacaj1202 , let me first provide some general rules ( and which will mostly answer your questions :(
(a) Rental income is reported for the year --- that is all the monies received as RENT ( received or constructivelly received)
(b) Rental deposits ( such as last month, security deposit, pet deposit etc. etc. ) are not income -- they are treated as escrow amounts and the use/ holding/ interest etc. are dictated by state law.
(c) your property is rented from the date it is available for rent i.e. when you start advertising ( formally or otherwise). And this date is important because your depreciation and personal use limits start from this date
(d) HOA, Mortgage, fire insurance and simliar expenses are to be allocated ( rental period vs. whole year for the first year at least )
(e) Utilities ( that you pay while the property is being rented is also allocated ( for the first year at least)
(f) repair, maintenance performed after rent start date ( see above ) belongs to rent account
(g) all these are reported on schedule-E
TurboTax will ask for these details ( when you tell it that you have rental property ) --- just go through the screens carefully. Note that for depreciation, it will ask for Cost basis ( acquisition cost plus cost of any improvements performed before start of rental period ), cost of land and thereby determine depreciable basis and the allowable depreciation for the year.
Hope this answers your questions --- if I have missed something and or you need more help, please write in comments.
