1, no, the relay is most likely not for the headlight. BMW did not use a relay for the headlight from the factory. The headlight gets it's power thru the high/low switch directly and it is fed from the "load shed relay" located in the electrical box below the fuel tank.
2, it looks like the blue item is a "male/female" factory splicing connector. What are the wire colors on each side of it, ie going "in" and "out".
Ok, so what do you have on the bike that appears to "not" be connected to something yet that uses 2 wires. Cooling fan? Water temp sensor? Horns?