I am a novice, but enjoying building my first cabinets very much!

The doors are built and ready to finish. They are made with 3/4 x 2-1/2 poplar rails and stiles and 3/4 MDF panel. I glued the entire perimeter of the panel for strengths since the doors are a little large at 24 wide x 29 tall. I will be finishing with BM Stix primer and BM Advance top coats. I am hoping you can help me with a few questions so I can get the best possible finish.

1) Is there ANY benefit to spraying the primer coats? I will definitely spray the top coats with my AccuSpray, but just curious if I can simplify things and brush on the primer (sanding after each of two coats) instead of spraying the primer. Would it affect the final finish at all? This applies to the poplar face frames also.

2) The routed parts of the MDF raised panel are rough. Do they need any pre-treatment, or will the two coats of primer and sanding take care of that, and allow the top coats to have a smooth appearance over the entire surface?

Thank you!