You can create new albums... and each album can have sub-albums. When you're in the album/sub-album, near the top on the right there's a box called "Share this album" - on the far right of the title there's a lick called "Share", if you click on that it opens a popup window and you can set a password in there. A sub-album can have a different password from the album it belongs to.
Be careful though if you move images from one album to another - if you do that, all the links to those images will change so any links you've already posted somewhere else won't work any more. So instead of moving those images you might want to consider uploading them separately to the new album.
If you want to delete an album or sub-album, along the Photobucket top menu go to My Albums, click on the arrow to the right, select "All Albums". On the list which comes up, you will see an option to Edit or to Delete against one.
If you want to delete an individual image, go to the album and mouseover on the image to see the delete option.
The Hubble Telescope has just picked up a sound from a fraction of a second before the Big Bang. The sound was "Uh oh".