Hi Jens,
Last year I had the same issue with NextGEN and I’ve found the solution after read lots of faq’s. (https://www.beinha.com/?page_id=11)
Here we go:
Question: I can’t see the thumbnails in FireFox , Internet Explorer show them correct.
Answer: This is an open CSS issue. Please have a look in your theme style-sheet and search for max-width: 100%;
Delete this line and the thumbnails are shown also in FireFox.
Source: https://alexrabe.boelinger.com/wordpress-plugins/nextgen-gallery/faq/
About changing between gallery and slideshow, I never tried but I’m quite sure you can do this with no problem.
Best regards from Brazil
Beatriz