Given your dandy description of the combination of symptoms, the best suspect is an intermittent connection. Specifically, follow the smaller battery positive wire to the under-hood fuse box. Be sure that connection is clean and tight. That connection has been a real common cause of this problem on most brands and models.
Even if that connection is tight, it's good practice to remove that wire, sand the terminal end on both sides, and the contact it's bolted to, then reattach it. Be careful that the metal tools you use don't contact that cable and any other metal part on the car at the same time as that will cause a dead short and a huge shower of sparks.
If that cable loses its connection while you're driving, the car's electrical system will still be powered by the alternator, but the battery will be out of the system. It is needed to help the voltage regulator maintain a safe and steady voltage. When the broken connection occurs, the voltage regulator may not be able to do its job properly, so system voltage will increase. You'd see that as brighter lights and a faster fan speed.
Some models also have a very large bolted-in fuse for the alternator. Those bolts are rarely found to be loose unless someone removed them previously. That could cause system voltage to drop down to battery voltage of 12.6 volts rather than remaining at charging system voltage of between 13.75 to 14.75 volts. That would cause lights to dim and motors to slow down when the bad connection occurred. That isn't what's happening here because that fuse is not involved with cranking the engine.
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Tuesday, March 9th, 2021 AT 1:02 PM