Should kids have play dates on weekends even if with kids every m-f?

Yes. Play-dates . allow you to monitor your child's peer interactions & teach age-appropriate pro-social & coping skills in a variety of settings. Tell your child what behaviors you expect, the rewards for complying & the consequences for non-compliance. If the kids squabble, calmly separate them or remove what they're squabbling about without blaming either one. Neurotypical 3-tear-olds have a preferred friend.
Depends. As long as they do their school work and whatever reasonable chores they are assigned, why not? We all like "down" time and socialization is generally a good thing. Children learn through play.