Assuming you're going to connect the DVD player to the Yamaha and then on to the TV via HDMI, as long as the cable from YSP to TV is of a similar quality to that from DVD to YSP, you'll be fine.
But to get audio from the TV into the YSP, so you can listen to broadcast TV via the sound projector, you'll need an audio connection from TV to YSP, as this won't happen over HDMI.
Depending on your TV, this will either be a pair of conventional stereo analogue connections or a digital feed (usually optical on most TVs offering this facility).
As far as a subwoofer cable, I wouldn't spend a fortune in this set-up - something like
this would be fine. It sort of depends what length you need, really...