No but a friend request would be a pretty cool feature. Also no there isn't a favorite author tab, but you could save the mangas you life of that manga with bookmark or with the other feature that lets you categorize it to "already read", "now reading", and "want to read".
Does the new site means friend request are now a thing? XD
Yaoi pals seem like a neat idea~! (Though I'm not logged in yet lololol)