It's quite possible that the previous tenants were just trying to keep the tub clean, but used one of those abrasive scouring powers - probably repeatedly - and didn't rinse the chlorine well afterwards. It doesn't really take too many attempts at trying to get the soap scum out to do quite a lot of damage to the surface, especially if you use one or the other of those things the porcelain people warned you about. Or maybe they just had a couple of bad batches of gin. (In some households, degreasing motorcycle parts has been known to cause visible artifacts.)

It's unlikely (not impossible) that your hairline cracks are the result of hot water. Most such cracks are the result of an "impact" or due to not having the tub on a solid/level surface, so that it's "bent" over a period of time - or flexed repeatedly in the same spot. I don't know of any generally useful treatment for them. Unless they're exceptionally ugly, the best procedure may be to think of them as the "signs of graceful aging."

There are "porcelain touch up" materials that applied properly can often render small "dings" nearly invisible. (They have a bad reputation because they are almost never applied per instructions.) Unfortunately, the repair won't have the same response to the soaps and other "bath accessories" as the surrounding material, so it will eventually begin to show; and may look worse than the original defect when it does. I've used them with some success on stoves and refrigerators, but the tub is a rather nasty "chemical" environment to expect much from them.

John