"I've submitted 4 initial question and these are the 4 I'd like the students to vote (rate) on and discuss. Do you think it might be possible for a student to have permission to view and rate, but not to add new questions?" - When you create the activity, set the, Approval required, to Yes. This does not keep a student from submitting an entry, but it will immediately make it unreadable to anyone but teachers, managers and admins. Tell students that when using this activty, they should elect to set their preference for, Unapproved question visibility, to, Hide unapproved questions. You can also just have the teacher, Remove, any unwanted entry by a student.
"When I "close" the Hot Question session, and still allow 'view', then it visually is what I want to achieve, but it didn't appear possible for a student to rate once it a close date was enabled." - That is correct. Students can rate ONLY when the activity has NOT been closed.
"Another option I tried was to allow the mod/hotquestion:view permission, but not allow the mod/hotquestion:ask permission, but the ask permission seems to be needed in order to enter the activity." - Again that is the correct behaviour that keeps guests from making entries.