Welcome to the club!
From memory my grandparents 1990 (carb 1.6) BG was a little slow to start when it was cold, but that one ate batteries as well, so it may have been related

(bad aftermarket alarm system!).
My current BG 1.6 (fuel injected) can also take a little while to get started when it has been sat for more than a few days, but just like yours starts with one turn when it's hot. My local Mazda specialist advised me the B6 engine can do this due to not having the most powerful starter motors (and age) but also said it's nothing to worry about unless it fails to start completely or does it when warm.
I hope someone with a few more years BG experience can pitch in their opinion too
Problems - Rust. Watch the sills, rear wheel arches and just general under-body. Also, suspension rubbers are typically quite worn and tired by this point due to age; I recently replaced the balljoints, track rods & anti-roll bushes and it makes it drive much better! Also watch for the bushes on the rear stabiliser, it will squeak and they are hard to find, my Mazda dealer is shipping them in from Belgium for me as they can't find any in the UK. It doesn't seem to be affecting the handling, however.
I hope I could help
