Yes. Continue the depreciation of the old property (now the new property) as though nothing as changed.
Yes. The buy up in your exchange (your New Property cost more than you sold your Old for), the answer is easy – you treat the additional cash part as you would a new addition to an existing property. In other words, you treat the amount of the buy-up the same as you would the cost of a capital improvement, placed in service in 2022.
Be sure to keep all of your records of how you arrived at the information on your tax return until you no longer have a rental property that was exchanged for another (sold).
@corinneL
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