2012 altima coupe 3.5 SR shut off while driving at 80 mph... could it be the fuel pump?

Purchased vehicle 6 months ago (new battery), so first time driving in winter… Two days before this event I tried to start the car and it wouldn’t turn, like the spark plug didn’t give out a spark but the engine was trying to start, but eventually did after i got a (unecesary?) jump from another car, and a ton of gray smoke came out of the exhaust for about 30 sec… I was driving a 2012 Nissan Altima coupe 3.5 SR manual (50k mi)… a few weeks ago on a very cold night… car started without a problem and I was driving for about 20 minutes and then on my way home at about 80 mph on the freeway, the car just turned off without my knowledge and I only noticed when I was unable to turn the steering wheel. No check engine lights, nothing…

By some stroke of luck I was able to avoid crashing into any major objects, but I’m just surprised as to how it happened or what it could be. Then I began to notice as the weather temperatures dropped around freezing that if i drive when the engine is cold, it feels like the engine or car is driving on a flat tire because of how rough or jumpy the engine could be like it’s stuttering.

Trying to figure out what this is, my limited knowledge and Google search results suggest a fuel pump. So I am baffled if anyone can help please let me know. Oh and FYI after those two incidents, aside from the stuttering from the engine and there hasn’t been any other problems related to shut off. I always use super gas and I don’t compromise on any fuel or parts used.