[moonchild]

> If someone posts something in your forum. Can you legally repost in twitter saying.. so and so just posted?

It may constitute fair use. Publishing their work in a book and profiting from it is another story.

> When you post in a public forum do you automatically assign the copyright as public domain by virtue of where you posted and who can see it?

No.

> Facebook owns all of the content you post (pictures/posts/videos).

As the sibling says, they do not.

> Doesn't this apply to all/most sites with user generated content?

No. A given website may state that as a condition of its use, users must assign copyright to anything they post to the owners of the company. This is not a common condition.