Found something in another post, that solved my problem with the “Oops! The game crashed” Error.
I had “citrix workspace” installed, that also added a virtual graphic device under my list of graphic devices.
I fully deleted citrix, so Hearthstone could use the right graphic device, and it worked properly. (Have had the same Problem with the Digital Board Game Armello, which also worked properly again from now on).
Even after I installed citrix again there were no further issues with Hearthstone.