The very short and quick answer is no you cannot use BrowserType.AspNetHost to test your Silverlight application. Net let me try to explain why:
Even if it did, to automate a Silverlight application requires use of the mouse and keyboard. If there's no UI, you cannot click on buttons (links, dropdowns, etc.) or enter text into input fields.
I'm sorry but I don't believe it's possible to test a Silverlight application headless. A visible fully interactactive UI is required.
For the other questions you asked:
Item 1) Answered above
Item 2) The path is required by the Visual Studio AspNetHost component. It will go to this path and load the application from that path into it's headless component.
Item 3) The SilverlightApplicationPath is only used when testing a Silverlight Out Of Browser application, one that has been installed on the machine and doesn't use the browser to run.
Item 4) Hopefully the reason this doesn't work is explained above already.