Yes. In order to achieve an even finish, new drywall must receive a full coat of primer. It seals the wallboard, the mud, the fastener patch, etc. It also serves as the adhesion coat which will probably last a lifetime if the wall is clean and dust free.

You can use a compatible primer or another brand of primer. SW, BM, PPG paints all offer a compatible primer. Zinsser is an excellent choice if you wish to use a another brand of primer.

A purpose-made drywall primer is cheap, and primed drywall is a lot easier to paint then unprimed.

Diluting paint to use as a primer is a poor substitute for the real thing.

If it's new drywall, then surely you taped and skimmed over the seams? Yes, you must prime new drywall. Look for primer especially formulated for this purpose, like freshstart.

Use a 100% acrylic drywall primer. PVA primers are not as good for adhesion or sealing. However, if you are intending to use a higher sheen finish coat of paint, two finish coats will probably still be necessary to achieve a uniform sheen.

BTW, you're welcome.

So now I have finished priming and have put the first coat of paint on, and some defects in the taping and/or mudding are showing up. Should I correct them and then re-prime and re-paint those areas? Most of the defects are small, such as dings in the surface, but one is a poor taping job - the tape didn't properly adhere and bubbles show up. I am inclined to cut and remove the tape then re-mud, prime, and paint. Comments?