I bought tickets for family as a gift but it is under my name and they have to pick it up at will call. Will they let them pick it up with an email confirmation and a picture of my id?

Yes. We've had no problems when faced with similar circumstance.

I would definitely call beforehand to make sure. They usually require the person who ordered the tickets there with a photo ID to pick them up

Yes

Make sure call first I don't think they would have a problem with that.

If not sure call.

Yes, let them know the person's name whom will pick up the tickets

Yes they will!