No; formal registration is not required for protection.
Works are protected by copyright as soon as they are "fixed." If you wish to register a work with the copyright office, you may do so.
Works are automatically protected once they are fixed, but you can register your art with the copyright office if you wish.
It is automatically protected as soon as it is fixed, but you may register it with the Canadian Intellectual Copyright Office (link below).
In Canada software is protected as a literary work under the Copyright Act of Canada. Copyright is acquired automatically when an original work is generated, the creator is not required to register or mark the work with the copyright symbol in order to be protected.
If you draw something, it's automatically protected by copyright. Otherwise... "register" is way too long.
To copyright a document, you can simply create the work and it is automatically protected under copyright law. However, for added protection, you can register your copyright with the U.S. Copyright Office by submitting an application and a copy of your work.
The songs are automatically protected by copyright as soon as they are fixed (written down or recorded), but if you wish to register them with the copyright office, yes, you can register a group of works under one application.
Business names cannot be protected by copyright, but you can register it as a trademark for $375 on paper, $275 electronically.
To copyright your educational materials, you can simply create them and they are automatically protected under copyright law. You can also register your materials with the U.S. Copyright Office for added protection and legal benefits.
To copyright an image, you can simply create it and it is automatically protected under copyright law. However, to have legal proof of ownership, you can register the image with the U.S. Copyright Office by submitting an application and a copy of the image.
In most countries, the work is automatically protected by copyright as soon as it is fixed. If you wish to formally register, you may do so after the work is fixed.
You probably wouldn't want to copyright a product; you might want to trademark it, or (if it's revolutionary) apply for a patent.