I use paints today that cure well enough to be machine buffed in 6 hours! Unless you got a "Pearl by Earl" cheapie paint job you are good to go, assuming you are talking about the car washes, and not a high powered 5000 psi machine.
Yes, the paint has been cured. Most shops will advise against polishing for a few months but washing is fine.
Power washing is never recommended for car paint. If it hasn't been at least 30-day, don't power wash. Hand wash it.
Never as in you should never power-wash a vehicle unless it is a farm implement, City bus or garbage truck.
I give up...... WHEN?