New York owners understand carrying cost better than almost anyone. Between property tax, common charges or maintenance, and a board that can veto a sublet, the annual cost of holding a Manhattan apartment before any mortgage is substantial. A Dubai freehold has a service charge and nothing else: no annual property tax, no UAE tax on rental income, no board approval to let it. That contrast, plus a direct flight, is what drives most New York enquiries.
Rules that apply to every buyer in United States are covered in the full United States buyer guide. This page covers what is different in New York.
Effectively no on the currency itself. The UAE dirham has been pegged to the US dollar at a fixed rate for decades, so a dollar-based buyer holds a dollar-linked asset. Your bank will still charge a spread and fee on the transfer, which is a transaction cost rather than an exposure.
US citizens and residents are taxed on worldwide income, so rental income and any gain on sale are reportable in the US even though the UAE does not tax them. Foreign bank accounts you open can trigger FBAR and FATCA filings. The property itself is not a reportable financial account, but the income is reportable. Confirm the details with your CPA.