Ceiling – the white flakes and hairy thing on ceiling

Per the wording of that code, you can't be adding anything to the floor or the ceiling as you'll be under the 7' minimum. You could consider a super-thin flooring (stain the concrete? Linoleum?) and then, as you suggest, put the sheetrock between the joists (though that sounds like a finishing nightmare).

Alternatively, raise the foundation (likely cost prohibitive).

All that said, I echo B Mitch...what is the concern of not meeting the code? The main drawback would be that you couldn't advertise it as finished square footage when you sell.

The first thing I'd do, though, is have an inspector come out and ask what the odds would be in getting a 1" variance or so. They may count it as 'close enough' and let you get by.

Do not prime the drywall before it is taped and sanded. Do all your drywall work first, then apply your textured coating. Normally there is no reason to prime the new drywall or joints before putting on a compound based textured top coat. If you intend to use a textured paint instead of a compound based texture, then you would prime the entire surface with a PVA drywall sealer/primer before applying any paint coat. Assuming the texture is compound based, then let it dry completely and prime this with PVA sealer/primer before painting. Do not use a regular heavy based primer or paint/primer product on your texture. Use PVA. The reason is that PVA is very light and dries extremely fast and if applied properly won't re-hydrate or saturate you texture causing possible damage. Once the PVA is cured, (usually just an hour or so) you can paint over it with regular latex paint without fear of texture falling off.