Does a tub/shower need a vent and also should a kitchen sink have a vent.

Yes and yes

Way back when I was learning the trade we plumbed our tubs through a drum trap and it vented through the tub waste and overflow. That was then and Harold nailed it. Every fixture that has a trap MUST also have a vent! The only exception that I know of is, that in my area, floor drains do not have to be vented. Good luck, Tom