First time doing rental property taxes. Need advice

[Grant H.]

I purchased my first duplex, out of state, over the summer and am now preparing to do my rental property taxes for the first time and have a few questions on deductions.

Is the home inspection deductible?

I initially had 1 vacant unit and had to cover the gas/electricity for 2 months. Are those utilities deductible? 

Do I need to report tenant covered utilities, like gas/electricity, as income? 

I switched property management companies after 2 months, for various reason, and had to pay a cancellation fee. Would that fee be tax deductible? I know that the monthly PM fee is.

I purchased the property without seeing it, but when I flew home over the holidays I went by to take a look. Could this allow me to deduct that plane ticket? I feel as if this is not the case but want to double check.

I pay no state income tax where I live, but the property I purchased is located in a state which has income tax - I assume I will need to file with that state.

I've done a good amount of research on what is a deduction vs. what needs depreciated but need more detailed answers on a few questions. Thanks in advance.