I am a resident of North Carolina and will be travelling outside US for a few months. Thus I will not be driving my car while gone. I'll either leave the car in a garage for storage or leave it for my cousin to drive. In either case, can I stop my car insurance and resume it after I come back to US?
I have done this frequently (with AAA), however it's not quite a full cancel, as you would probably want to leave insurance against theft/flood/etc. (will be required if you don't own your car outright) but it will drastically reduce the rate.
There are also two "flavors" of doing it, you can tell them until when, or you can leave it at "until you inform them otherwise", which will typically end up with you paying less right now but an equivalent amount as the other option by the end of the year/term.
Also plan on the insurance only being able to be changed on a work day, i.e. if you return Saturday, and plan to drive Sunday, have it with driving insurance on Friday (or see if you can schedule it for Sunday).