My brisket is going to come off about my bedtime. Is it safe to FTC it overnight?
I would not recommend it. If it is well wrapped and insulated you could go 3 or 4 hours. You do not want the meat to stay a long time in the danger zone.
Is two hours long enough to leave it in?
When I do take it out of cooler, do I need to put in refrigerator until morning? Would putting in oven be safe?
Fridge.
You want to hold meat either above 135* or below 40* to be safe.
I would put it in the refrigerator. I think it would dry out in the oven.
I have done up to 8 hours on a pork shoulder with no problems
It will also depend on the size of the meat.
Squirt provided the key for safety.