"Do you know those classmates?"
I don't know if that would also be correct, but at least you would usually not use them, as xie already shows that there's more than one.
The rule that's often cited on the internet is that "们" isn't used when there's already a pluralizing measure word (e.g. "些").
There are differing opinions as to whether it should be used when there isn't a pluralizing measure word but it's still clear from the context that the noun refers to the plural. However, we can at least say that it wouldn't generally be considered wrong to use it in such a situation. (To some extent it's probably a matter of getting a feel for it, though.)
Yes, as the object pertains to people/person. Otherwise, the given Chinese sentence is being general with 同学
No. As the question is asking whether the listener knows the classmates, it is natural to expect that the listener may know some but not others, rather than knowing or not knowing them as a collective. Definitely it is not correct to use 們 here.
I should give some examples that using 們 is alright:
It's possible, but I don't think it would be likely in the given sentence. For people, it can be used for "know of (someone)", rather than "know (someone) personally".