If you have your own car, the entrance to Petra is about a 10 minute drive away. The hotel runs shuttles, but I didn't note the times as I didn't use that service. If I recall correctly, I saw 4 frequencies in the mornings and 4 in the afternoon?

Breakfast starts at 6am. We would have breakfast when they opened and get to Petra well by 7am.

Best piece of advice is to book Petra properties EARLY during peak season. Hotels were essentially fully booked 3 months out (the Movenpick was my first choice). I snagged the last rooms at Aicha Memories Camp in Wadi Rum too. The Marriott released award inventory closer to my date of arrival, so I'm glad I was able to switch my paid reservations to awards.