I think it would stick to the iron. I would use a damp pressing cloth to be on the safe side.

Yes rinse it until all the water soluble stabilizer is out!

I have always rinsed out my fabric and FSL items before pressing.

It depends, sort of. If you are doing FSL, you don't want to wash it out completely as you want it to be stiff, but sometimes it doesn't lay as flat as you want. So after rinsing just enough to get the visible stuff out, I'll iron it but I'll put a pressing cloth under and over it so it doesn't get stuck on anything.

I usually have to put things in the washing machine to totally get rid of the wws stabiizers, but sometimes I don't want to do that, or I want the design to have a crisp look to it like it has been starched. So I rinsed it well and let it dry. The fabric will have a stiffness to it, but not board stiff. Then I steam iron it face side down on a folded terry cloth towel. I do this all the time and never have a problem with it.

Thank you for your advices