1) It is a violation of the AMA rules to allow non-members to use an AMA facility. This can jeopardize the clubs AMA charter. Yes, you should ask them kindly to post their AMA card on the frequency board. If they don't have one you should ask them kindly to leave. Not fun, but it must be done. Besides, if you can afford a plane or heli then you should be able to afford a ~$48 annual insurance policy! There really are no valid reasons to not join the AMA.

2) You should check with your City/County park dept and verify if there are any regulations prohibiting RC aircraft. Most likely there are not. In addition, if you are an AMA member then you are insured to fly where you wish. As long as you have permission from the landowner be it private or public land. So, check with your local govt agencies but I think your model store owner is full of it!! Sounds like he wanted to sell you an electric.