@BookHoarder: After some more try and error I learned, that with this sequence in the metadata code, series info is always displayed correctly on my Inkpad.
Code:
<meta name="calibre:series" content=""/>
<meta name="calibre:series_index" content=""/>
<meta name="calibre:rating" content="2"/>
<meta name="calibre:author_link_map" content=""/>
<meta name="calibre:timestamp" content=""/>
<meta name="cover" content=""/>
<meta name="calibre:user_metadata:#gelesen" content=""
The only time it was not, I just had to shorten the metadata comments. It seems the Inkpad 3 doesn't like long comments.
It is important that you don't push the "update metadata" button, after you have done the sorting of the meta name! I save my ebooks to the Inkpad via "save to disk".