Photo Stream & iCloud turned on - but Photos taken on iPhone don't appear on iPad
Photo Stream definitively only works for photos (or screenshots) taken after it was enabled.

As for your other problem: Yes, if you are logged into the same iCloud account on both devices and have Photo Stream enabled it should sync whenever you are logged in into a Wi-Fi environment (apparently Photo Stream doesn't sync over 3G).

What else can you try:


Take a screenshot on the iPad, make sure you are in a Wi-Fi environment and see whether the screenshot appears on the iPhone
Log in to iCloud from your computer (requires Lion or a recent Windows version of course) and see whether the photos get streamed there