1. Yes, if you know how to do it properly. 🙂
2. It's how I have things set up with my Mac mini. Since iMac is a desktop computer, the external drive can be connected all the time; as long as your iMac and external drive a powered ON at the same time, it will be like having your iTunes data on the internal drive.
3. I don't understand this question.
4. You can use network storage (like Time Capsule) for your iTunes storage, but using a directly-connected external drive is preferable. Why? Because access to network storage tends to be slow (and less reliable), compared to a directly-connected external drive. Even a cheaper USB 2.0 drive is MUCH faster than network transfer speed, especially over Wi-Fi.
5. Yes, you can use Time Machine to back up your internal drive AND directly-connected external drives. By default, external drives are excluded from backup, but you can set Time Machine to include (not exclude) the external drive. You cannot include data stored on network storage in the Time Machine backup. However, you can back up your Mac's internal drive and external drive to the Time Capsule using Time Machine.
Here's how I have it set up. First, if the external drive is not a Mac-specific product, it is probably formatted for Windows. Use Disk Utility to Erase it. When you do this, select the drive in the Disk Utility sidebar, not the volume indented below the drive. Then Erase it. The default settings for the Erase re-initializes the drive for use with a Mac.
On the external drive, create a new folder called iTunes Media. Do not manually copy anything into that new folder. It should be empty at this point.
In iTunes preferences Advanced pane, where it says iTunes Media folder location, point that path to your new iTunes Media folder on the external drive (use the Choose button). Below that, checkmark the TWO boxes for Keep iTunes Media folder organized AND Copy files to iTunes Media folder when adding to library (if they are not already).
From the iTunes menu bar, File -> Library -> Organize Library -> Consolidate Files (checkbox), and OK. This command "consolidates" all of your media files (from wherever they are currently stored) and organizes them into the designated iTunes Media folder (on the external drive). By letting iTunes copy its media files over to the new iTunes Media folder, iTunes keeps track of its media files. You can use Finder to see how things are organized.
After this operation completes (it could take a long time with a large library), iTunes is accessing its media files from the iTunes Media folder on the external drive. You can spot check some songs by doing a right-click Get Info and going to the File tab. Make sure location shows a path to the external drive's iTunes Media folder. You can also move the previous (old) iTunes Media folder to a different location (like to the Desktop). If iTunes keeps working properly, iTunes is accessing its media files from the external drive. You can then delete the old iTunes Media folder to free up the space on the internal drive.
If anything above is confusing, please post back...