1.) At the moment I am using sqlite as database. Is it possible, that I can access the sqlite file on the harddisk of my user to read/save data? (on User dir its possible but access an USB stick ?)
If you want to use a local database then you'll either need to install your Silverlight application on the local machine as a full trust application or use a database that installs into Isolated Storage like SiaqoDb (as suggested by @Shawn Mclean). You won't be able to access a USB stick.
When run in a browser across the net it has limited access to the local hard drive for security reasons. If you're doing this you might as well stick with WPF.
2.) Is there anything concerning MVVM silverlight can not handle?
You can use Prism to develop MVVM applications for Silverlight as well as WPF.
3.) Does SEO work well with Silverlight 4?
I don't know a great deal about this, but Silverlight can be viewed as Microsoft's version of Flash so it will probably have the same SEO issues as Flash. The code is compiled and delivered to the client in binary form, so unless you split your application across multiple HTML/ASP.NET pages there won't be anything for Google to index. Apparently Flash does support SEO, but I haven't looked into SEO and Silverlight.