1. Generally speaking, as long as the rest of your 2018 tax payments (withholding, estimates) are at least equal to your 2017 tax liability you should be able to wait until next April to pay the taxes. If your 2017 AGI is over $150k, then the current year payments will need to be 110% of the 2017 liability. This is one of the safe harbor rules (and the easiest to plan around in my mind).
2. You should take depreciation in 2018. Rental property is on a mid-month convention, so you will take four or five months in the year of sale.