When you take a photo it should only go two places.
The camera roll; always.
Photo Stream; if you have it enabled in Settings > iCloud > Photo Stream. Each of these places is separate, and you will need to delete photos from them separately.
The purpose of Photo Stream is to make the photos you take available on all your devices (and computer if setup that way). If you don't need or want that, turn it off on all the devices and computer. Photo Stream only keeps the last 30 days or 1000 pictures. I'm not sure which cuts off first, since I've never gone over either.
When you delete a picture from Photos Stream it should end up deleted on all devices. The computer should keep all photos unless you delete them there. Hold in mind that since the updating is happening over the internet, changes may be delayed by a slow connection or one or more devices being off line.
You may see copies of a photo in other places, but these are only copies.
If you create an album in Photos on the iPad (as opposed to syncing through iTunes) the album consists of nothing but links to the original photo. Deleting it there deletes it everywhere. That will not affect a photo in Photo Stream, since it is not a link, but a completely different copy being synced from iCloud.
The All Photos tab is that. Every photo, whether in album, camera roll, or Photo Stream. It's not a copy or a link, just another way of viewing the photos.
I hope this helps.