Kitchen Large Electric Appliances - Over the Range Microwave

I just installed my Over the Range Microwave between two 3" end panels. I find that when I open the door the hinge side of the microwave door slightly hits the 3" end panel. I followed the template included with the microwave and the microwave ended up being flush with the front of the 3" end panels on both sides. Is it normal for the microwave to be flush with the front of the fillers? Or should the microwave stick out some to allow the door to open freely?

If the end panels protrude further than the cabinet door above the unit, then it is not normal. Generally there is no protrusion beyond the front edge of the cabinet door. If it opens, you are lucky.

The end panels and the cabinet above are both 15" deep - same as microwave. Seems that most other kitchens only have 12" upper cabinets so the microwave would normally protrude past the cabinets by 2-3".

The microwave I installed is flush with the end panels and cabinet above without the doors on it. Should the microwave be flush with the cabinet doors? If so, that would probably be enough clearance for the microwave to open without hitting end panel.

I guess I would have to remove the microwave support bracket and build it out by the thickness of the cabinet door. Or put a piece of 3/4" plywood on the back wall then attach the bracket and microwave to that. Would that be ok?

What you are suggesting with the plywood may work just fine. Be sure you secure the plywood to the studs. Most of your weight on the back is vertical, and the screws through the top cabinet do most of the holding.