When you support and arm terror Groups in your neighboring country then you should be prepared for the consequences. Refugees will surely find a way into Turkey, Turkey cannot shoot at everyone trying to escape the conflict zone. You reap what you sow
No way, Russia might hit Turkey occassionally and vise versa. It won't cause major conflict since Turkey has made a little tilt towards East.
They are not in that position to Ask for such thing. Syria on the other hand is getting stronger day by day like an iron turning to Steel under continously pressure. There is no month that Syrian airdefense doesn't engage with Israeli missiles and fighters, they engage with Foreign supported elements, they engage with Kurdish separatist Groups supported by USA and Gernmany/France.
The time of weaponizing refugees has passed long time ago. USA is weaker than anytime so the NATO card doesn't exist for Turkey.