Partial response: you can convert your project to a Java project by adding the following nature to the .project
file contained at the root of your project:
<natures>
<nature>org.eclipse.jdt.core.javanature</nature>
</natures>
And I think that the purpose of the Checkout as New project is to be able to create an "Eclipse project" for a project that has no .project and .classpath file. This allows you, for example, to say that the project is actually a Java project.