NOT A TEACHER,
Because you are a teacher, I have to say that I am reluctant to help you answering your questions, but I guess it does not hurt.
1. I have never heard of things such as "supposing that," and "granting that". For "providing that," I GUESS it can be used to start a sentence.
2. I don't know if "giving that" actually exists. Is it possible that you may be confused with people saying "given that", but it sounds like they said "giving that?"
I have no comment on your fourth question.