Many (most?) airlines list the aircraft type during the booking process. Even for those that don't, you can look up the flight number and date on a site like FlightAware or SeatGuru, which will tell you.

But, if the airline needs to, they can swap out the scheduled aircraft for another one at any time up until takeoff. So you might book with the belief that you'll be on a 737 NG, but get to the airport and find (or not even notice) that you're on a 737 MAX.

You can see it in most search engines, and after the Ethiopian crash Kayak announced they'll add an aircraft type filter. Other flight search engines will probably follow suit.

Yes, you can find out which plane you are going to fly on. .