DVD audio is a PCM format.
Any digital connection is going to convert the DSD to PCM. At the rate of change there may be a preamp or receiver with a DSD decoder out there, but I'm not aware of one. If someone knows there is shout. I know for sure my universal player can only output from the DSD decoder after DSD conversion via the analog ports and it is HDMI 1.2. For anything else there has to be a PCM conversion. So yes, to hear true DSD you need analog cables.
The bottom line is that if your player is outputting SACD in digital , or provides bass and level management, then there has more likely than not been a DSD to PCM conversion.
In terms of up resolution, where possible it is best to let the TV do the up conversion.
As far as listening modes it all depends on your set up, so I can't comment.