No.
"Should we approach his teachings with the same skepticism he's just
advised to approach everyone else's teachings with?"
Yes.
"On what authority does he claim that his "opinions" are any more
valid than everyone else's?"
The same authority we all claim. Vicious circle, isn't it?
"Is it all relative?"
You'll need to explain this question further. Because relative
connotates relations. Which tends to lead to the Golden Rule, which
would then seem like yes. Then again... :)