2000 Honda Accord Car start/drive issue

I am not sure of the services needed. It was suggested by a towing individual that the issue is "possibly" the alternator. I "YouTubed" information and the likely issue is the "main fuel relay". The car was "jump" started and stayed on until the car was parked. The car had to be "jump" started again to restart & move the car. The heard shutter suggests that the car would have stopped as previous, if a longer range of driving was attempted. Please see comments below.

The interior indicator lights began to dim, milage no longer present on dash, drive strength of the car noticeably decreased, and the car shut down & would not restart after slowly approaching a turn signal. 2 days prior, car was parked in the heat/sun. 1 day prior and on the day of the starting issue, all interior dashboard/indicator lights remained on during entire the drive. I would like to know of the potential problem to better prepare for the repair costs.