It is more common to refer to TV resolutions by their horizontal resolution - hence the term '4K'. However yes with HDMI 1.4a all current Macs are limited to 2160p which is the vertical resolution of a 4K display.
For playing movies in most cases you probably will not notice much difference between 30fps and 60fps, however if the movie is encoded at 50fps and you play it at 30fps this creates a mis-match that does not allow a simple multiple to compensate and can lead to juddering. For non-movie use especial normal computer use and especially scrolling it can become intolerable.
With regards to Displayport at 4K and support for 60fps, originally Apple stated the Mac mini 2014 model like previous Mac mini models did not support this. Only very recently have Apple changed their 4K article page to change this information although at this point I have not seen actual user test results.
The Mini Displayport 4K to HDMI 2.0 adapter you listed is a different make but basically the same solution as the Club3D adapter I listed for you in my previous reply. Therefore my previous comments on this will also apply as quoted below.
This adapter will convert Displayport 1.2 to HDMI 2.0 and therefore supports 4K at 60fps. It claims that it itself supports HDCP 2.2 but this is actually in terms of allowing HDCP 2.2 to 'pass through' your computer would also have to support HDCP 2.2 to benefit from this. I mention this because some 4K material will be protected by HDCP 2.2 and I suspect that even on a higher model Mac that would otherwise support 4K this may be a problem. Your own material recorded with a camera would not be protected by HDCP.
Since Apple do not themselves provide any 4K material via their iTunes Store - they currently only provide 1920x1080 as a maximum, it is I feel unlikely Apple at this point provide any support for HDCP 2.2.
