Can anybody provide information about buying phones from AliExpress?
For example, will they work with most carriers?
Will they work at all?
Will they have the latest operating systems?
Will they run more apps than other flip phones?

There is no general rule of "phones from AliExpress" as each phone will have its own unique features/compatibility.

Is there any sort of "rule of thumb"?

cowculator Generally not going to work on Verizon, sometimes At&t, more often T-Mobile,
most run various versions of android. Will anything you buy from Ali work? Its a gamble