The warning light needs to work, so renew the bulb, the blue wire as you know goes on the "IND" of the terminal for this.
It will normally start to charge if revved high enough, this is a built in safeguard.
The B+ wires normally go direct to the battery, on some cars they go to the starter feed, as this is direct from the battery too.
If you unpick the insulation you'll find they are actually joined together in the loom, into one wire that is thinner than the two reds were, and the soldered joint will be absolutely covered in corrosion.
Engine grounding is totally adequate, as it needs to be to operate/supply earth to the starter anyway.
tabetha