These are, in the end, all fairly easy questions that you'd have found the answers to with a quick search of here or Google, but...
I and II) I don't see why you would not be able to do so. It's only a matter of writing the necessary client-code to contact the server. I've written test classes that stand-alone to access web-services we've written, so I do not know of any reason a Java SE or Portlet couldn't do the like. (I would, however, add as a caveat that I have no experience with portals, and this is just a theoretical "common-sense" answer on my part.)
III) Yes. As long as you avoid one or two pitfalls with your serialization, you should have little difficulty communicating between .Net and Java using web services. We've implemented solutions in our office that go both directions.
Theodore Jonathan Casser
SCJP/SCSNI/SCBCD/SCWCD/SCDJWS/SCMAD/SCEA/MCTS/MCPD... and so many more letters than you can shake a stick at!