It is very normal to have to fix flaws in new drywall after primer. Most of the minor stuff you can't even see very well until a coat of primer has been applied. All you need to do is spot prime the patches, then apply two coats of finish and you should be fine. The repairs that look like a bunch of tiny bubbles comes from laying the mud on too heavy.

So HD doesn't sell those cardboard shims in-store (online only) so we bought 1/8" hardboard (?). Seems to work great for using as fillers and getting the drywall flush.. hope this material is OK! Other issues we're encountering if anybody can shed some light: it's super difficult to get the drywall screw into the joists. It starts off great and easy and then about 1/2" away from being countersunk, it squeals and is super hard to push in the rest of the way. We're using those drywall setter bits and we've literally gone through 5 just putting up 2 boards of drywall (maybe 18" x 36", not very big boards). Is this a problem with our joists or screws (we're using 2") or even our drill (DW 18V cordless)? also - due to this difficulty, we've accidentally embedded the screws a little TOO deep in our efforts to get it countersunk (as we're pushing past this "tough" spot, some times it just goes right through!). I hear everybody say "NOT to rip the paper" and "not to go past countersunk" but some of our screws are definitely at least halfway sunk into the drywall board (1/2" thick). Is this a serious problem or are we OK with 1-2 "bad" screws per board? We're putting 4 screws per joists for each board of drywall...

Fresh start latex, primer. regal for the walls , the waterborne ceiling paint for the ceiling.

Primer is not paint so try not to treat it like paint. They used to have clear primer that worked great. Paint is basically glue and pigment (when dry) most primers have a lot more glue than pigment and some fillers to mask rough spots. Most modern primers will have some kind of sealer to even out the high absorption of drywall and the low absorption of mud. Personally I prefer separate primer and sealer but time is money. Paint on the other hand has a lot more pigment than glue. Primers create an even yet (microscopically) rough surface for paint to stick to.