Did you scan from inside or outside?
I can't remember what teardrop is, so I don't know :)
Only if the connection attempt was initiated from the outside.
The blocking at the router protects your internal machine(s) from contact initiated from the outside (a.k.a. the big bad internet) It's an important element of security, but far from the only one.
To respond more directly to the title of the post, whether you need a firewall in addition to the router depends on your needs. My firewall blocks all connection attempts from the inside other than the few expected ones (http, smtp, etc.) in addition to not letting anything in from the outside. But I'm just paranoid.