Plasmas do have burn in issues but it would not be a problem unless you have a still image in place for a long period of time. Realistically, that's not likely to occur. However, the black bar issue would be something that would concern me. I will defer to the experience of others on this.
With respect to the brown out question, I do not think it is the brown out itself that is a problem. Rather, it is the fluctuating voltage, i.e. the drop in voltage that causes the brown out, and then the spiked increase in voltage when the brown out ends. These fluctuations in voltage can damage any electronic equipment, not just plasma TVs.
As for warranty coverage, read what the warranty says. I would not believe anything the kid in a big box store says about it, unless he's a law student moonlighting for extra money.