As a screen reader user I don't like content above the main heading. Normally I navigate by headings so would miss the error message. A better solution is to output an h1 heading above the error message, then leave the rest of your headings in tact giving you two h1 headings.

It's completely up to you. You can either put them in the header or not, as long as the elements within them are internal navigation elements only (i.e. don't link to external sites such as a twitter or facebook account) then it's fine.

They tend to get placed in a header simply because that's where navigation often goes, but it's not set in stone.

You can read more about it at HTML5 Doctor.