If you buy a entry ticket and a wristband can you leave the fair for something and come back the same day and still be able to go back in?

Sure can! You'll be stamped on the way out

Yes. On exit, make sure to let them know and they will stamp your hand for re-entry. If the stamp washes off they may not let you back in.

Yes

They will stamp your hand at any of the exits if you just ask and then you'll be able to come back in without having to buy another ticket

Yes but you need to inform them that you need to leave but are coming back