You can only take the days as the annual vacation after USCIS received the petition (Receive date). Before that, you are not authorized to work.
And futhermore, how to explain this gap when next to seek for a new H1b petition because they ask to give out the timeline while I stay in States?
Don't write the date. Just write mo/yr in the time line.
Should I require a normal statment from Uinversity for future use?
Not recommended. Even it is your HR's problem to delay your petition, it is your responsibility to keep legal status.