This thread is for asking Scott questions about the awesome Sunchaser setting. Hopefully he drops by here at some point.
Lets see if I can help
1.) What do the non sun-worshipping Vessans and drakes follow? I understand its some religion dedicated towards ancient dragons but what are its characteristics?
The Dragon Kings alignment shown in table 3.3 is both the faith of the Drake in the Black peaks and that followed by the Vessan.
2.) What happened to the Vessan princes who joined the Sharos? Are they still princes?
They are still 'princes' in the sense that their bloodlines are revered by other Vessans and they hand down a small amount of secret knowelege and religious ceremony - they are still responsible for going out and making certain minimal offering at the shrines of their tribes but it is a practice maintaned more for traditional reasons than religious. Their alignment is predominantly the Eyes of Heaven. An occasional throw back who secretly or not so secretly holds the old ways in their heart rather than the faith that brought them into the human society could make for a strong NPC. I see a Vessan Firebrand promoting a return to the old ways as a good hook for adventuring, but most are happy to work and live shoulder to sholder with Humans and Green Erron.
Having players track down and win the favor of either of the two current Sharos princes might make an excellent prelude to a player gaining levels in the Ironfang master class - not because the Princes are themselves Ironfangs, but any 'civilized' masters of that art may require the approval of a prince before they pass their teachings on.
3.) Do Green Errons and Vessans become hazelighters as well?
I don't see why not. Its a religious calling not unlike being a paladin and both the Vessa and Erron have produced true-believers.
4.) It seems that all races are represented in the Sunchaser setting except for the giants (even if some are in the army of darkness), are they in there? And if they are not in the setting at all, where would you advise that they be put in (should the need arise)?
Sunhaser is set up to absorb new character options very easily, so giants can be introduced as player characters or a one-off threat as easily as saying "And then one stumbles out of a sunpool." They are not intended as a sustained
threat or pressence in the setting - partially to differentiate it from the norse-inspired Godspawn. If you did want to add them on a full-time basis I would sugest small communities high in the Rainwall mountains.