Invites
 

Is there a way to invite for say a Public Quest from the General Chat? other than typing weird names and such?

Just click their name in the chat channel
 

I don't know that your question is considered DARQUI specific, but I know you can left click on a persons name in the chat channels and you have options from there to INVITE, SEND A TELL, ADD TO IGNORE, etc. That may be all u need to do, just click their names in the chat channel...