I would think that illorum might have been used due to its implication of distance, although it does seem that both would work. Pronouns can be tricky though, particularly in Latin with its large number of pronouns.
Yes and no. Read the dictionaries and grammars. Pronouns stand in for something, and part of the problem here is that there is no context for your exercise sentence (“Their territories seem broader than ours.”).
So ille is for a third person that’s present and is is for a third person not present? I had assumed that. But now let me ask you all, was there anyway of knowing which word to have used in the sentence? It could have been either of the two, am I right? I mean, how could I have known whether their was a group of people that were present or not present. Am I correct?
“Their” as opposed to “our” calls for illorum, not eorum. If ever there’s emphasis on “their” (as there is here), illorum will be appropriate; if not, eorum or nothing.
It’s not really a matter of presence/absence. Ille is the opposite of hic; it distances.