How old was Harry when he left the Dursley's residence prior to the Battle of the Seven Potters? If he had just turned 17, why leave by broom/flying vehicle instead of using a port key or Floo Powder? 2nd part of my question, why leave by magical means at night when he could have taken polyjuice potion or used his invisibility cloak and transport himself via non magical means like the tube or taxi during the day?
Harry left the Dursley's residence just before his birthday (not after it) so he still had the trace on him.
In answer to your second question, they tried to leave at a time that the death eaters were not expecting (gave false leads and such) and the dead of night is perfectly viable for stealth. The only reason it didn't work is because they were "betrayed". Blending in via normal transport may have worked, but it would have put Harry at a larger risk, for a larger amount of time, and if they had done that and been betrayed then they would have not been anywhere near as prepared to defend themselves.