It is not possible to change an image in 'edit item':
a) I firstly delete the OLD image (that was already there) with 'check this box to delete...' and press 'apply'
b) K2 refreshes screen and shows content-tab, i move back to image-tab, which now has no image
c) I press 'browse server' and select a another image and press 'apply'
d) K2 refrehes and inserts the OLD, deleted picture again.

Any ideas?

Just tested on live server 1.7.1 k2 2.5 browze server works ok for me and replaces image. I would try reinstalling k2 and testing.

can I re-install over the existing installation or do I have to delete the old one first?

"Always backup First!" New iphones language translation translate this string to "Use Akeeba"
then install over the top of existing installation

OK, partially successful. Images can now be selected an replaced in the back end. Thx so far.
Installed version now is K2.50

Unfortunately now the frontend/Browser doesn't show the images properly that are configured in the backend-items while changes to text are beeing updated correctly.
Images hold on to strange behaviour:
a) deleting an image results to an accordingly update on frontend -> no image is shown
b) then selecting again a (different) image in back end -> old picture beeing shown on frontend, while backend (item) shows the newly selected image.

This may be a caching issue

Well, good answer ;)
if so, what could I do to either make sure or solve my problem?

Latest info: images are beeing updated after a certain time.
I'll open a new thread for that 'caching issue'.
Thank you William!