Well, I would say fix that issue, and your other problems will probably go away.
It could be a problem with the configuration of the WDM in Windows Audio Shared Mode. I assume NYA streams only in Shared Mode, using a browser. There is no App for it that can use Exclusive Mode, right? ... Or maybe there is, if you are using the OraStream player?
The Windows Volume Mixer should show that it is playing to the WDM, and MC's Audio Path should show what it is receiving. Set the WDM Default Format in Shared Mode to something that always works.
If using the OraStream player in Exclusive Mode, then make sure the WDM can play what is being sent to it. The WDM driver supports both 16 and 24-bit audio up to 192kHz, and only supports PCM.
For example, using your current process, I could see what is happening as;
1. You start playback in NYA to Windows, where the default audio device (the WDM) isn't available. So Windows chooses to play to another audio device, if it can, but regardless the NYA player starts in Shared Mode, because it can't take Exclusive control of the default audio device.
2. You start MC. The WDM accepts the audio in Shared Mode, because that is how it started, and there is no trigger to switch NYA or Windows to Exclusive Mode.
So, if you are using the OraStream player, and it is set to play in Exclusive Mode, configure it to play in a format that the WDM supports. i.e. PCM in 16 or 24-bit up to 192kHz.
If the OraStream player streams in say FLAC native format, then that is a different situation altogether.