"Do they know their students?"
Translation:Czy one znają ich uczniów?
Yes, although it has slightly different connotations. „ich” would me more like "somebody else's" students, while „swoich” can only ever mean "their own".
No. "swojego" could be used, if it described something masculine and animate: swojego człowieka, swojego mężczyznę, swojego chłopaka, swojego psa, swojego studenta. Here you have "swoich studentów" (masculine personal plural) or alternatively, "swoje studentki" (not masculine-personal plural). The English sentence has plural "students", not singular "student".
It is my understanding that it is a gender difference. "One" is for a group of all female and/or neuter nouns (I think, neuter; someone may need to correct me). "Oni" is for groups with at least one masculine noun.