How do I create "static" fields like page header/footer, that appear on each page but so that editor only has to enter the content on one page, and that same content is shown on each page where that field is used?
I also need localization on that field, is that possible?
If the content in the header/footer will be the same all over the site, you could create these fields as properties on the start page. You can then use the PageLink property on the Property web control to fetch the property values from the start page. You might want to put these properties on a separate tab called "Global settings" or similar to avoid mixing it up with the other start page properties.
Don't forget that you need to databind the EPiServer:Property web control if you use it to get the property from another page than CurrentPage.
If you want to be able to have different values on different parts of the web site, you could use dynamic properties instead.