(1) How i can change the size (a little bit smaller) of the Groups? I need 5 in a Row.
You can't, there's no set amount of entries per row. It's entirely dependent on the space being available. So you need to make the component container bigger by modifying your Joomla template.
(2) How i can change "suche Kategorie", "search Categorie" into "Suche Stadt", "Search City"?
By changing GJs language strings. See the below for language usage information.
www.joomlapolis.com/localization
You maybe able to use a language override plugin as shown below.
www.joomlapolis.com/forum/6-news-and-publicity/227556-cb-language-override-video-tutorial-resources
(3) How i can integrate the Postbox from uddeIM in this menu?
If it's a tab then simply change its position to a non Nested one and it should show there. Review the current tabs there for their display and position parameters.