1. The backup most likely completed normally. There is no dialog box indicating the completion. The screen saver will have no effect on this. If you want to know the date and time of the last complete backup click the Time Machine menu icon:
2. Yes. The "star wars" display shows you a picture of whatever you happened to have in the frontmost window when you entered Time Machine, and all its backups through the oldest one that exists. You will not have much to look at until a number of backups occur (by default, once an hour). If you want to restore an individual file or folder, navigate to the one you need and click "Restore". If a newer copy already exists in the same location on your Mac, Time Machine will ask you what you want to do with it.
Bear in mind Time Machine is a backup utility. It is not an archiving utility. If you delete a file from your Mac, it will be deleted in Time Machine eventually. This could be as little as one hour from the time you deleted it from your Mac. The deletion of backup files is a function of Time Machine's clever algorithms.
3. Time Machine is one option. It is probably the easiest backup method to use, is wonderfully integrated in OS X, but offers little in the way of customization or configuration. Use it for a while and you will become familiar with it.
Individual photos in iPhoto are not easily retrievable in the current version of iPhoto. If you need to retrieve one or more individual photographs without altering your existing iPhoto Library you must restore the backup iPhoto Library to an alternate location. Choose that Library when you open iPhoto, export the ones you need, close iPhoto, open the existing Library, and import them. It's a clunky workaround but that's how iPhoto works now.
Music is a little easier. At least as of iTunes 10.x, you can still navigate to individual music files and folders if you need to restore them.
If you want to augment Time Machine with another backup method, consider Carbon Copy Cloner. It is not free, and it follows a very different philosophy. It is a good idea not to rely upon one and only one backup method. I use both.
For answers to just about any question you could imagine regarding Time Machine, avail yourself of Apple Support Communities contributor Pondini's Time Machine FAQ.