Docker is for deployment, it works in terms of graphs of filesystem images. The tools do slightly overlap in use case, but they operate in entirely different domains.
It wouldn't be unreasonable to mix both in the same project, but there is no hard rule for when this would be appropriate.
Not really, it's just a tar file with some metadata. Using fpm¹, making packages from a directory is extremely simple. I've been building internal packages from our different components, and the build script only has three or four lines. And besides, even Dockerfiles often use apt/yum.
This is a problem for Go programs, due to multiple unversioned (usually) dependencies on other Go libraries.
I'm not going to be building .debs for installation inside Docker containers (turtles all the way down) but I would still consider something like aptly for storing and managing any obscure dependencies that my applications might require, and for maintaining a mirror on the local network to speed up image builds.