PLeavitt,
I think that you have two different reactions taking place in your water heater.
The hard, white deposits are calcium from hard water. You can cure that by using soft water. The more practical solution is to drain the deposits from your water heater periodically. I would not drain via the T&P valve. That's the safety valve with the lever on it. I would de-pressurize the water system, ensure that your water heater contains cool water, and remove the drain plug. Then open the T&P valve to allow air into the water heater. This will increase the flow out of the drain plug. There are two reasons for using the drain plug. First, you don't risk getting a piece of debris stuck in the T&P valve and holding it open. Second, the calcium deposits are at the bottom of the water heater tank and so is the drain plug.
If desired, you can stick a coat hanger wire into the drain plug to try to scrape as much of the junk out as possible. You could also turn on the water pump (or hose) and allow the water flowing into the water heater to help rinse it out.
If you can switch to soft water you will eventually eliminate these deposits. Not only will they stop forming, but the existing deposits will eventually dissolve. Soft water will also dissolve any of the hard water deposits in your valves and other plumbing fittings.
I suspect (but am really just guessing) that the pasty deposits are from something else. My guess would be reactions with the sacrificial anode rod.
Here's my opinion regarding whether or not it's required: First, if the manufacturer installed it, it's probably a good idea. Second, if it is disappearing (meaning it's working), then it is definitely required. If that rod doesn't erode, then something else will.
Loren