I haven't specifically noticed that problem with Portlet Bridge 3, but we haven't been testing RichFaces with it at present as the focus for 3.0 is JSF2 support.
We're currently in the process of determing which RichFaces 4 components do and don't currently work with Portlet Bridge 3, so that we can resolve them in 3.1. Unfortunately an initial release of that would be about a month away at best.
In the mean time, if you can debug through Portlet Bridge to see the requests for stylesheet resources, you may be able to find an easy resolution that you can propose a pull request for, so that the fix can make an earlier release.
the following: After if I defined a head-tag and a body-tag, the styles are not missing. But I think it is not the right way in a portlet, do define that tags.
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
I think it is not correct to define a head and a body. Here I recognized that reRender will not perform.
And if I try the portlet way like this, the styles are missing:
<?xml version="1.0" encoding="UTF-8" ?>
What you need to remember is that you're writing a JSF 2 application that uses RichFaces 4, and not directly writing a portlet.
The goal of the Portlet Bridge is to enable you to write a portlet as if it were a normal JSF 2 application. To that end, the head and body of a JSF 2 page needs to be defined, otherwise it isn't a valid JSF 2 page. The Portlet Bridge then takes care of only rendering the content of the body of the page back to the portal container.