In answer to your question, "Do all foster kids have issues?"
As a former foster kid myself I would say YES, (but depending on the circumstances prior to foster home, different levels of severity) purely because the life I had known, mother, father, siblings, was ripped apart, and siblings sent to different foster homes, mother never to be seen again, etc. There were issues, such as not being able to trust, not being able to bond, not being able to validate or talk about how I was feeling. Probably the biggest issue of all for me was ANGER. Anger at the whole wide world...for I did not choose for my life to be this way, it was chosen for me, by, yep, ADULTS. Having no choice leads to frustration, helplessness, and that leads to anger. I am NOT saying bad behaviour is acceptable, but it is understandable, given the circumstances.
Saying this, SOME of your foster kids behaviour does sound like normal kids acting up, pushing, to see what they can and cannot get away with, in my experience, most kids do this to a certain degree...
Really listen to Dadfor2's advice, he has hit the nail on the head, and in my opinion knows from experience EXACTLY what he is talking about, he has a very good feel for foster kids and their emotions, shame he wasn't my foster dad a few years ago!
Collette