The little light (and traction control lettering) (at the floor shifter) stays lit all the time during everday driving.
When the button is depressed (to put out that light), another light then appears at the dash which reads "traction control off".
Is this correct, "traction control" lettering light always stays lit alongside floor shifter?

Yup, that is the correct behavior.

The light by the shifter will stay on while traction control in engaged. When you press the button it will diengage traction control. This will then throw the warning light on the dash on. Like Teoubk stated, that is exactly how it is supposed to work.

Just feel glad that you are able to disengage it when you want. Not all cars can, and there may be instances where it is nice to have it off.

There is also a safety feature built in that will shut the traction control system off on its own if the computer thinks its hurting more than its helping, or if the Traction control has been on long enough to where the computer thinks it is going to overheat the front brakes.

I realized this one morning on my way into work when I used to work at Advance. It was a nice snowy NY winter day and I came flying into the parking lot (with all my co-workers watching and cheering from the window of course ), but the parking lot was complete Ice and snow, and I had my foot down hard and was trying to turn. Next thing I know the "hmmmm" of the traction control that you normally hear when its on was gone, the "Traction Off" light was on, and I jumped form like 2k to 5k RPM'*. I tried pushing the button, etc.. but it would not come back on. I thought I might have broke something, but as soon as I turned the car off and then back on again everything was normal. I've had it happen 2 or 3 other times since then, and every time its happened I was squealing the tires on pavement or spinning them in the snow pretty hard, so the guys at my dealership were right when they told me it was normal and a safety feature.

Just thought I'd inform ya