Do public events give XP? If so, how does it scale based on location or type of event (Kill target vs Defend the thingy)?
The first public event you complete each day rewards you with a package at the postmaster. Opening this package grants 5,000 experience. For completing the event itself, I do not think there is any known experience gain, besides whatever you get for kill enemies. If you get some at the end of the event itself, I do not think it is a significant amount, otherwise people would probably have figured out a way to exploit this and power level.
Events give 500 points. I played with 2 others in a Defend the Warsat mission. I had the 9000-without-dying bounty on, killed myself with a rocket to drop it to 0, and waited without killing anybody and got 500. You can just do 2 patrol missions to get 500 (one gives 250, though target missions may give more, since they offer 25 vanguard points instead of 10).