You should disconnect or remove the old regulator . alternator needs unfused battery current to the + terminal at all times , even with key off .
_Some_ alternators need another lead from the ignition circuit to exite the field windings and make it charge @ idle speeds .
Asking for a Delco " SI " typ alternator @ your FLAPS will negate the needs for the secondary wire .
There should be much written on this in the archives including schematics and diodes needed for some setups , not all .
Fan should have a relay that's wired live and has a temp switch in either the upper tank of the radiator or the thermostat housing , I got a thermostat housing from a 80's vintage Camaro as it has a bung in it ofr the fan switch so it'll switch on after I shut the truck off and it begins to heat soak , runs 5 ~ 10 minutes depending on the heat .
If you have a pusher fan , delete the stock fan , don't need both , pusher fan _must_ be wired to stay on anytime the AC clutch is engauged .
Stock radiator is way overkill for any V-ate so if still running too hot , have it " rodded out " flushing is a wa$te of time and $ in every case .