Dane wrote:My home page has the title "Die neusten Fotos" (engl. The latest photos), which is as far as I want - on my page. But on Google it is also displayed that way. This may be a bit confusing. Can you somehow adjust that Google for the home page something else is displayed?
Google will mainly use your page's <title></title> tag in search, which by default is populated by your page title by X3. However, this is where X3's page SEO settings are useful. From settings > page, scroll down and expand "SEO":
If you popuplate SEO > Title, this will be used in the page's <title></title> tag instead of the title that is on page. The <title> tag is invisible to humans, and is only used by search engines for indexing. In this field, you should write a title up to 60-70 characters, that best represents your website, and which you want to display in search.
Dane wrote:The description is simply taken from the footer, including the designations of the social media links " Share on FacebookTweetPin itShare by EmailDownload. ShareShare on FacebookTweetPin itShare on LinkedinShare on ..." This is not so good and does not look like a serious site.
Normally, Google will simply use your page description tag, or some text on your page that it finds appropriate. Since you don't have a description for the page, and since you only have image-captions on that page, in this case it just takes the first text it can find, which is in the footer. You should definitely write a page>description ... If you don't want it visible to humans, or you want a different description on page than for search listings, you can use the SEO>Description field, which populates the <meta name="description"> tag.
PS! After making changes to your page, it could take a few weeks before Google re-indexes it.