Does this have sulfate and can you use on kertian hair?

As a brand representative for IGK, I will be happy to answer your question! All IGK products are formulated without sulfates SLS and SLES, making them safe to use on hair that is Keratin treated. I hope this is helpful!

After using product and drying hair, does it help keep hair smooth in damp, foggy weather?

I have very thick, curly, frizzy hair if I just dry with no product. This does help. Put on wet, then dry hair, then spray more on each section you flat iron. I still get curl in damp weather but not so much frizz. Maybe if I put more on but doing my hair is such a project. Try it. It does smell GREAT. If you don't like it just send it back. Best product I've found so far that at least does something. Otherwise, get a Brazilian Blowout. THAT DOES WORK BUT $$$ at the salon.

Should I use this spray before or after I add gel, other curling products etc(I always apply to wet hair)?

As a brand representative for IGK, I will be happy to answer your question! If using in damp hair, it is recommended to be applied before gel. I hope this is helpful!

Is it oily on fine thin hair?

As a brand representative for IGK, I will be happy to answer your question! Good Behavior Smoothing Spray is suitable for all hair types and is heat activated to aid in smoothing when applied to damp hair before blow-drying and in dry hair before styling with hot tools. You can use it either, or both ways! As long as it is used properly with heat, it should not contribute to an oily feeling in the hair. I hope this helps!