A relay can give you a brighter light, but will not reduce the current use. It will save the current that poor connections and corroded switch contacts can waste and deliver it to your light, but the battery will still be seeing the same demand. The relays I use are standard Bosch style "cube" relays, but there are smaller Panasonic relays available fromm Mouser, DigiKey, or Eastern Beaver.
The LED taillight will draw less current, but if your system is positive ground you will need to find a positive ground LED light.
The original single phase alternator does not put out much current at low rpm, so if you run headlights around town, it will have a hard time keeping up. A three phase alternator puts out more current, but more importantly will produce more current at lower rpm.
The small light in the headlight is a parking light which is turned on by the toggle switch on the headlight bucket. Many riders in "headlight on" states use a halogen bulb in the parking light and use this as a daytime running light. I have a halogen main bulb in my Interstate with a 3 phase alternator. It will putter around Daytona for an entire Bike Week without need for a boost from a charger. A 3 phase is a worthwhile investment if you run a daytime light or do much night riding in town.