*Partial Answer*
1) Cocoa supports SOAP services, so if you have an ASMX service (or a WCF service with a SOAP endpoint) you can. See
http://www.icodeblog.com/2008/11/03/iphone-programming-tutorial-intro-to-soap-web-services/[
^] of course the devil will be in the detail, the more complicated the stuff you are doing the less likely it is to work out of the box.
2)As far as I'm aware the iOS is pretty much Linux based, so you can store things in the file system. Obviously you'd want to do this on demand (i.e. not download all docs at the outset). You should also consider a document cache size limit.
3) Don't understand your question.
4)You can convert PDF, the resulting text can be sent via e-mail. There are 3rd party tools out there, I dare say a google search will uncover some open source stuff.
5) The thing to do here is to poll the server for updates from the client. I don't *think* you can push data out, for one thing the device isn't certain to be on a network at all times
6) Don't know.