There are a lot of tutorials about error 404 handling and different solutions.
If I'm using TYPO3 6.1, Fluid/Extbase and RealURL, what is the best way to make an Error 404/500 handler that uses the page Uid = 13 (error/notfound/)
If you have an error 500, TYPO3 will not be able to handle it since it is "crashed". For 404 handling you will see a list of possibilites in the install tool, section [pageNotFound_handling].
The most straight-forward way for a website with one language is to enter an absolute URL to the [pageNotFound_handling] field. The URL could point to a TYPO3 page or a static HTML site. TYPO3 will not redirect to this page, but output this page and send the proper 404 status.