Car shut off on me while driving?

So prior before shutting off a few days earlier it was hesitating to start. It did this twice where I had to turn the key and then release it and try and again, until it fired right up. It was the first day of cold weather and I believe it was -5.
Last night I was driving and the car shut off as I was in third gear cruising at about 60 kms.
I pulled over and then it started right back up again BUT I noticed my battery light flashing, and then once it started the battery light disappeared. I messaged my step dad and he told me to clean the clutch sensor, so I'm thinking about trying that. But that wouldn't explain why the light was on flashed? He then said it could be the alternator but that wouldn't make sense because chances are it wouldn't have started back up again. Anyone have an idea on what this could be? The car is an 04 Honda Civic if that helps.

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