How many months of interest/taxes can I deduct for my rental property?

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Some details: I purchased a rental property in April; because it took a few months to complete all repairs it wasn't available for renting until September.

I have two questions:

1. I'm allowed to deduct mortgage interest, property taxes and HOA just for the last 4 months? (September-December) or for all year?

2. Can I depreciate appliances even if they were purchased before September? as in July-August.