Does one need to have a period to get a std?

No: No, literally all you need is skin to skin contact for most STDs and contact with infected secretions for others. That means any skin to any skin, even oral to genital or hand to genital contact. For instance, one can get the virus that causes genital warts from anothers hands, and one could get gonorrhea in the throat from oral sex. Periods have nothing to do with it.

No: An std is contracted by having intimate contact with someone who is already infected. Having a period has nothing to do with contracting an std.