How can I see my Apple ID email / contacts without installing iCloud? I don't want to install iCloud on every work or borrowed PC I happen to use, but would like to be able to read my mail and contacts related to that Apple ID.  Isn't there a way to simply use a browser to read my email and see the contacts, like Gmail or Outlook?
Yes - https://icloud.com has web apps for mail, contacts, calendar so you don't need an OS X or iOS device to use them. Several modern PC and Linux browsers are supported.