Not that it's going to make (b) any better, but do you have purpose-made tyres on it? I've never tried with my road one, I heard it was loud and wore down extremely fast if you did so, so I just bought a smooth (and I think harder?) one designed for use on a trainer off the bat.

Could just be marketing and I fell for it, but seemed reasonable.

Re (b), and especially if you changed tyre, I suppose if you wanted to do that regularly you'd soon get a second quick-release rear wheel, so you didn't have to faff about switching skewers (and tyres!) - or better a 'direct drive' trainer (instead of running the bicycle wheel against another wheel, it comes off and you put the chain directly around a sprocket attached to the trainer).