Changing the order of the clauses is no solution. I think what you want - or your teacher wants - is clause equivalents:
1. After opening / (After) having opened his supermarket, Jone has been working 15 hours a day.
2. (When) asked to tell the story, he cleared his throat nervously.
3. Having (had) no map, they got lost.
4. Not wanting to interrupt the speaker, I adjourned my question to the break.
I can't think of an acceptable clause equivalent for No. 5 because the subordinate clause is causal and has its own subject (I). Perhaps something like
He did not go out on Friday owing to my advice will do?
Cheers
CB