Difference between photostream and icloud photos

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

Photostream will store the previous 30 days worth of photos automatically. That means, every photo you take on your iOS devices will be sent to Photostream, but only the last 30 days worth of photos will be available there.

If you enable 'Automatic Import' of Photostream in iPhoto (Preferences > Photostream > Automatic Import) then when you launch iPhoto, it will automatically download a copy of any photos that are in your Photostream, and automatically create an Event titled: {MMM YYYY} Photo Stream (eg. "Jul 2012 Photo Stream")

This Event will be automatically kept up to date, as long as iPhoto is open long enough to sync everything required (depends on your connection).

In effect, as long as you open iPhoto once every 30 days and leave it open long enough for your Photostream to be imported, you should never have to manually import a photo from your iOS device at all.

As for removing items from your Camera Roll on your iOS device, as long as you see that they are present in Photostream (or in iPhoto), then it is safe to delete them from your device. (There is no way around this but to do it manually as far as I know.)

Currently, Photostream does not support videos. To import videos, connect your iOS device to iPhoto and import these manually.

As a side note, in order to keep some photos on the device, you can create a smart album in iPhoto along the lines of "Photos taken within the last 30 days" or "Photos rated 4 stars or more", and configure iTunes to sync these to your device. That way, you can be sure that no matter if you clear your Camera Roll on your device, or delete certain photos, you maintain some convenience.