Don't you have to register a copyright to make it copyrighted?  If it doesn't have a copyright notice... it's not copyrighted!"

WRONG.
The moment any work is actually CREATED it is automatically copyrighted.  Therefore any artwork or fiction you see on the net or otherwise is ALREADY copyrighted to the owner, no matter whether the copyright is registered or not.  The official law on this is anything created after April 1, 1989 is copyrighted and protected, even if it doesn't have a copyright notice on it.

Don't you have to sign something for it to be copyrighted to you?  I mean if it's not signed or marked it belongs to anybody right?

WRONG.
Signing it only makes it easier to prove your copyright.  It does not make something copyrighted.  Once again, the work is copyrighted the moment it is created.  Just becuase something isn't signed doesnt mean you can take it.  If you didnt make it, or originate it, you CAN NOT TAKE IT.

Isn't everything on the internet public domain?

NO.  Everything on the internet was created by someone. Meaning it is copyrighted to whoever created it. It is NOT free domain, unless the original creator gives you permission to use it.

I'm just using a few images... and I'm not making any money off it.

You didn't ask permission or get permission from the owner.  You can't use them, no matter how few.  It doesn't matter if you're making money or not.  Copyright means the right to copy.  It doesn't mean the right to make money.  If you are copying or using their work without their permission then you are violating copyright law no matter whether you are making money off it or not. The only exception to this is when images or other copyrighted material is used in the form of either parody or used in a small amount to illustrate a point.  To illustrate this the difference would be between a site saying "Hey! I love Disney's Hercules movie!" and next to that text telling about their Hercules love, they have a picture of Hercules.  This is acceptable. It's covered under "fair use", since that image is being used to illustrate what they are talking about.  (magazines and various critics do this all the time). However a whole archive of Hercules pictures would not be considered "fair use". 

I don't have a scanner, but I want to make a picture of my character, so I changed the color of this drawing I found, so it's mine now.

You are directly violating copyright law.  Not only did you take the artist's image, but you modified it without his/her permission. On top of that you're claiming it as your own.  Just becuase you don't have a scanner or you cant draw does NOT mean you can steal someone else's work, or change it in anyway.  And that's what it is. STEALING.

Fanfic is not a copyright violation, I made up the story.

WRONG.  Fanfiction is a "derivative" work.  If you are using characters that belong to someone else without their permission, then you are violating copyright law, even if its just fanfiction.  Be aware that most creators (like movie and tv show companies) don't mind of people write fanfic, BUT  it is their choice.  You do not have the RIGHT to fanfic, nor do you have copyright to your fanfic. It is a derivative work.

My postings of their images or works are just helping promote their work! They should thank me!

So?  You're still violating copyright law.  If they agree to let you "promote" their work, then it's fine. But if you didn't get permission, you are still violating copyright law, no matter whether you think they should let you or not. Even if what you are doing seems to be a good thing for the original creator, you must ASK them first.  It is their right to determine how and where and when their work is used.

Still not clear on the law?  Check out the Outposts for more details on copyright law.