I repeat...........
Is there any water down below IN the sink cabinet?
Truthfully, I still can't really tell what is going on- if that is a water line stain and the silicone has gaps at the counter level, it could be that. Again.... it could be minor unless you see WATER or moisture and if the faucet "needs tightening" call back whomever installed it. For all we know, it's much ado about nothing. What brand is the faucet, where was it purchased etc? What part is loose, handle or base of faucet at counter level.
There are no mind readers here, and no...none of these issues have any affect on your counter tops.
Basically? Your best bet is call the plumber on the whole thing. If the under mount sink has no strap beneath? Have him address that as well.
Q