I don't know about the Server software, although I believe reading a Microsoft document stating that you can do that, but as far as the .Net framework is considered - 2.0 is not an upgrade to 1.1, it is a rightful departure from it, and thus they will coexist very peacefully on the same computer. I'd search the Microsoft knowledge base about SQL Server 2000 and 2005 Express, there should be something authoritative about it there. I, too would be curious to find out how it actually works.
You can definitely run SQL 2000 and SQL 2005 on the same machine, but any one machine can only have one default (un-named) instance. As long as at least one of the two uses a named instance (which Express uses by default), you'll be fine.