Hi Bolshevik,
Welcome to the macProVideo.com forums :)
The Streaming service (online access) and HD download service (using NED 3.2 for Mac) are quite separate.
The online service can only utilise your browser and the downloads must be downloaded and played using NED.
For more info on this please read the 'About' page:
http://www.macprovideo.com/about/nedweb
If you need to increase the size of the video window you can try using a lower Display resolution or even zoom in (Control and scroll wheel)... but this won't improve the image resolution.
I'm surprised to hear that the resolution is not satisfactory - could you tell me which tutorial you are watching.
Many thanks
Rounik