electric fan ???

Are you sure 13 A is the steady current? It may just be the starting surge. You need to rate your wires and relay for the surge, but how much it requires from the battery depends on the running current and duty cycle. A cheap, reliable fan that many use is a Mercedes pusher. My 64 Valiant came with one, but I got another at the junkyard (~$20), plus the little horns on the mount bar. I will put the 1st fan on my Dart.

I wouldn't change the alternator until you know it is insufficient. Watch your ALT meter as you drive. Put the battery on a charger once a week, and if it charges fully in <10 min, you know your alt is keeping up. Caveat - a bad battery (sulfated plates) will show fully charged quickly too because it can't "hold a charge". I have the round-back alt on my Newport w/ EFI and AC and it works fine. Once it didn't and I found the alt was getting weak (1 of 3 diodes was blown).