Can DotSVN be used as an independent component?

Sure. The idea is to create a 100% compatible (at the repository level) port of Subversion - very similar to SVNKit (which is a pure Java Subversion client library).

Similar to SVNKit, you can use DotSVN, when you need to access or modify Subversion repository from your DotNet application, be it a standalone program or from an Asp.Net web application.

What is the current status of this project?

The latest status of the project is given here.

How can I contribute to this project?

DotSVN project has just started, so any help would be appreciated. The easiest way to join the project is to post your query in the project discussion group.