I figured out that the mouse wheel problem was caused by a tool I use:
http://ehiti.de/katmouse/ I disabled it now and I'm able to scroll vertically now with the mouse wheel. One mystery resolved... I'll disable Katmouse for MultiDataViewer, although it is a very useful tool to scroll unfocused windows with the wheel. Some apps are incompatible, one is Google Chrome. Looks like MultiDataViewer is another one
Regarding the scrollbar. I resized the window, made it smaller and vertical scrollbar did appear. However, the size seems to be wrong: I dragged it down and I'm still at about 50% of the file (see screenshot1).
Then I increased the window a little bit, and the vertical scrollbar disappeared again (see screenshot2).
Arrow keys work in all cases.
This is a Win7 x64 machine, with DPI set to 125% - not sure if this matters. Did not cause such issues so far, though.