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The sensor in the tires takes a battery and the battery might be bad or the tires were filled with air that has too much water vapor in it and the sensor is affected by the water.

Yes it does and it is important for aircraft tires and tires on higher end race cars but for the average motorist it is complete a waste of money.
It is a means for tire dealers and others to "upsell" customers to a very profitable product that they do not need and will be of very dubious benefit to them. Don't let them con you and here is why if you are interested in reading further.

1. You cannot get pure nitrogen in your car tires unless the tires are completely free of air to begin with and then filled in a vacuum. But they are not. They have air in them when they are filled. Further, unless you test the nitrogen going into your tires from the fill station you have no way of knowing if it is even 100% pure and often it will not be because of quality control issues..

2. Air is about 78% nitrogen in any event. Most of the rest is Oxygen and the remainder other gasses including Co2. Oxygen leaks out through the walls of the tires very slowly over time and what is left is a higher % of nitrogen. Then when you add air to your tires the oxygen in that air will slowly leak out and the cycle continues. So over time, just by adding air to your tires as they slowly lose some pressure, the % nitrogen content will increase as the oxygen will continue to very slowly leak through the fabric of the tire much faster than nitrogen which is very slow.

I saw one independent test which tested the pure nitrogen content of 2 tires, one that had a fresh nitrogen fill and another that had only used air over a couple of years. The tire which had only used air to fill it had a higher nitrogen content. Nitrogen fill = BIG FAIL in that case.

3. If you have paid for a nitrogen fill and you check your tire pressures and find they need topping up are you going to drive around to find a business with nitrogen available or are you going to just top up with air any how? Most people will just add air because they need it now and the gas station is open and convenient.

4. Aircraft and higher end race cars will use nitrogen rather than straight air primarily for one reason:
The pressures in the tires will not increase with heat and decrease when cold. They are stable.
Stable pressures are important for aircraft tires and for race tires(because the handling of the race car can be sensitive at high speeds to small changes in tire pressures. Funnily enough I never used nitrogen in my race car tires and nor did any of my competitors when I was racing. We just did not bother and set our tire pressures knowing how much they would quickly increase after a couple of laps).

But that is not an issue for passenger car tires. You fill them cold at or above the recommended pressure and, when you drive, the tires warm up from friction and the pressure increases by a few pounds which is not a negative issue. When the tires cool, the pressure drops slightly which again is not a problem because you always set your tires pressures cold. When you need to add air you can and you don't have to find a business that can do a nitrogen top up for you.

5. For 15 - 20 dollars you can buy a good tire gauge which you can use to check you tire pressures cold. When you need to add air you can and it is free. Normally I just over pressure the tires by a few pounds at the gas station and adjust them at home with my tire gauge when the tires are cold. It is simple and just check your pressures every 2 weeks or so at home at your leisure with your tire gauge.

Paying a bunch of money for a nitrogen fill and then having to pay again when you need to top them up is ridiculous for a road car. Using Nitrogen is no guarantee against slow leaks in your tires which can occur with a slightly faulty tire valve or a very tiny puncture or a leak under the tire beading where the tire wall contacts the wheel rim. So using Nitrogen does not alleviate the need to regularly check your tire pressures anyhow and to then adjust them when they drop below the recommended pressure or below your preferred higher tire pressure.

6. Finally the proponents of expensive nitrogen tire fills will tell you you need to use nitrogen or your wheels will corrode. They claim that the tiny amount of water vapour in air will cause condensation inside the tire and cause the inner surface of your wheels to corrode. This is complete nonsense. Your car will be dead long before your wheels will corrode from that. Any wheel corrosion that is possible from failure of the layers of paint protection is much more likely from the outside of the wheel which is totally unprotected from the elements, brake dust, scraping the wheels on kerbs and gutters, harsh wheel cleaners etc etc. I am yet to replace a car wheel due to corrosion, let alone corrosion on the inside of the wheel rim protected by the tire. Have you?

Yes they do.........The nitrogen filled tires a great for hotter and colder climate.........Hope this helps...........Also less condinsation in tires.

The sensors are pretty dependable. You have to make sure that the tire pressures are on the money. Check the door jam for the correct front and rear pressures. Don't go by the tire, go by the door jam or owners manual. At times when the outside temperature changes a lot it can cause the light to come on.
You may want to check the tires for defects, punctures, or a bubble/s.

You are not going to do any harm mixing. The only thing is, if you are going to fill with nitrogen, if you have to fill up with air in an emergency, get the nitrogen refilled at your earliest convienence. Why pay the money and waste it. It shows here you are inquiring with an SUV. I wouldn't bother. If you had a sports car of some sort that you wanted to increase handling charactoristics, I would say go for it. With an SUV just keep the tires rotated(every oil change is pretty convienant since it is already in the shop), double check your tire pressure every week or 2, keep the vehicle aligned every 6 months, and every 2nd oil change, have them check for proper wheel balance(it changes as tires wear).