I was wondering, if the fact that in German Kurrent script the small letter "e" looks similar to the small Greek letter "eta" is just coincidence? Both look almost like the "n" that we use nowadays.
It is not quite clear to me whether you are talking about Greek printed script or (Modern) Greek cursive handwriting. In German humanistic education only the former was taught. The modern cursive script is used only by Greeks and did not influence the way Greek was written in Western Europe. So I do not really see any way that Modern Greek cursive script could have influenced German handwriting.
In Greek printed script the letter eta always has a right leg descending below the line. The Modern Greek cursive eta (ita) generally does not have this descender, so it does resemble the “e” of Kurrentschrift. But, for the reason indicated above, this has no relevance for the history of Kurrentschrift.
I don't see a similarity there. IIRC, when we learned to write it (in elementary school, class 4), which was probably the modernized version called Sütterlin, we wrote it without the connecting stroke in the middle it seems to have in internet resources. Maybe that's something only done in printing, or I do no longer remember it correctly. It's quite some time ago.
A similarity appears to be more so with "d" and "delta", I would say.
Nonetheless, you are probably right. All the European alphabets will be related, hereabouts they did not invent the wheel twice.