My television is a Panasonic Th-42PX60. The optical output specifications for my TV only tell me that it is Dolby Digital. Not sure as to whether or not that is 5.1 capable or not. I would think so.
The answer is not so simple. When watching anything from the internal ATSC tuner, the full signal gets passed out the optical out on the TV. So for example, the prime-time shows that are broadcast in 5.1 will get passed out the optical port in 5.1. The Vizio soundbar will give you an error in this case and you will hear nothing from the optical port.
However, if you have an HDMI source, like a Satellite receiver or Blue Ray, it's not so simple or nice. Multi-channel DD gets passed to the TV from the HDMI connection. but at that point, the TV down-converts the multi-channel out to DD 2.0 to the optical out. So you will lose multi-channel sound going through hdmi into the TV. I don't think all HDMI TV's act this way, but the Panasonic ones do. I can't speak for the newer models either.
To answer the first question my cable box and my dvd are going to the TV using HDMI cables. My cable box is a Pace 787X for digital cable and I have a Panasonic DVD Recorder VCR combo. Thinking of going Blue Ray in the future. I figure they'll be down to almost $100 for Christmas. The optical is the only audio from the TV to the Soundbar.
You need to realize, with this configuration, you will not ever get more than stereo out of the TV into your soundbar. Maybe this is fine for your room. The Sony soundbar is actually a 3.1 system, so you get a discrete center channel in addition to the stereo sound on 5.1 sources. The Vizio is a 2.1 system.