If there's a picture of someone in a public profile on a website, can I copy that picture? Can I post it? Can I use only a first name with the picture? Or is it atomatically copyrited by the person who's profile it is? Or do you have to file for a copyright on that picture?

The answer is not cut and dried.

Here are a couple of resources about this subject:
http://www.tasi.ac.uk/advice/using/faq_images_internet.html
http://www.utsystem.edu/OGC/INTELLECTUALPROPERTY/mmfruse.htm
http://en.wikipedia.org/wiki/Wikipedia:Image_copyright_issues_for_dummies

To Rick's answer, I just would like to add it depends on which country you live in.

I know that Canada and the USA have somewhat different laws on Copyright.

If you are in the USA though, I would say that you CAN copy the picture. I watched an episode of Judge Judy and this exact case came up. This woman posted a picture of a guy on her website, and put his first name. Then posed the question, is he hot or not. And her website viewers posted their comments.

He sued over that. Judge Judy told him she has a right to post his picture, but she is responsible for the content that her website viewers post. But then Judge Judy said, why are you so mad? These are all POSITIVE comments. But she asked the woman to be polite and take it down.

In Canada, it is also a grey area. If you are not using this picture to make a profit, then you are OK. Once you start deviating from that line, the clouds get very grey.

If the person who made the image is a pro photographer the image is automatically copyrighted and it is a violation of the law to reproduce it in any way without the owner's permission.
Prairie Son, retired pro photographer