Playdates can be easy or a nightmare from hell. I think it really depends on the child.
My youngest used to have the most quiet, lovely playdates. Girl would come over, they'd go to the playroom, I'd hear quiet conversation, they'd come eat a snack and return to their lovely games. She somehow always chose friends who were like this - to this day, at 11, when she has friends over, they're quiet, polite, just a pleasure.
My middle child, also a girl, has always attracted loud, boisterous friends. Their playdates were always full of running around, playing for 5 minutes then "they're huuuungry…can we pleeeease have a snaaack?…we're boooored, mommy, can we paint? bake something? play with water? glitter? make crafts? can you help us?" ALWAYS high maintenance and always loud. The girls are also very nice, just very exhausting. And now, at 13, it's the same. Her friends are loud (you cannot imagine how loud 13yr olds can squeal when they're delighted about something), outgoing, constantly moving, etc. Nice girls, but OMG, are you serious?! Calm down already!
As for the stealing, I don't think it's uncommon for a 7yr old to "borrow" something. Not saying it's right, just that it's not unheard of still at that age. I'd continue to keep an eye out when that kid comes over or perhaps just cut back on playdates with him.