Virtual Theme allows you to switch themes based on virtual paths, making an entire site accessible through multiple themes based on their URL prefix.
Yes. There are options to enter a Blog Title and Tagline that will override what is specified in 'General Settings' for a given virtual path.
Yes. Use the Add Virtual Path form to specify a single virtual path and select the theme to use from theme drop down menu.
No. Widgets are defined at the site level and will appear on all supported themes. However, almost anything is possible from within theme templates and you could just alter a theme template to omit or allow certain widgets manually.