Student or Learner
The following in red is confusing.
Teacher #2 wants to use questions to stir up her students' thought process, and to ask questions of their own.
Is it saying "the teacher wants to make students ask their own questions"?
Yes, it does mean the teacher wants to make them ask their own questions. "Of their own" is the same as "their own".
However, that sentence does not make sense; cutting out the middle bit, it reads "Teacher #2 wants to use questions to ask questions of their own." That is nonsense, and should be "Teacher #2 wants to use questions to make them ask questions of their own."
PS: Apart from that bit (which may or may not be from you), your English is very good – I'm impressed.
[Not a teacher]