Drain the hot water from the system by opening a 1st floor bath faucet (or basement faucet if your HWH is in the basement). Then it looks like a simple brass screw union so you should be able to replace it yourself. That's an electric power vent motor right behind it so be careful with water around there.

You might also want to strap it to the wall as it could be putting pressure on the pipe connector at the top of the HWH.

I drain my tank from that drain on the heater. I attach a garden hose and run it out to the street. I then shut off the water supply to the tank and unfasten the water supply line. This will aid in draining the water faster because it is excruciatingly slow. I actually built a fitting that screws onto the supply line and then connects to my air compressor and I usually charge the line with about 50-75 psi of air and then it drains quite nicely. I am told it can take much more pressure, however it is much faster than just gravity so it works for me. Besides if it can't take it I am the one who has to repair whatever could not take it. I am pretty sure the tank itself can take it, but it's the plumbing I am concerned with. I do this every year just to remove sediment and make the tank last a bit longer.

Since it isn't soldered, just turn off the main and open a valve somewhere to depressurize the pipes. Turn the HWH off, drain a few gallons of water out so the water level is down and out of the expansion tank. 'Unscrew' it. Put the new one on using Teflon tape on the threads. Turn the water back on and let the tank(s) fill. Turn the HWH back on.

Before you install the new thermal expansion tank, you need to adjust the pressure in the new expansion tank so it matches the water pressure in the plumbing in your house. Here's a link to a YouTube video that explains how to do that.

The rust spots may have been caused by the leaking expansion tank. There is a lot of rust along the edges of the tank. How old is it? What is the indoor humidity? It is unusual to see a the outside of a tank develop rust like that.

The rust is on the outer jacket of the hot water heater. Treating the rust spots is not going to affect the life of the inner tank in my opinion.

You could open up the flush valve every few months to remove any sediment. Run the water until it is clear. Set to water temperature to 120 degrees. Running it hotter reduces the life, but running it colder increase the risk of legionnaire's disease.

My previous hot water heat I bought in Sears lasted 19 years. I rarely ever flushed it. From my experience a hot water heater life is reduced by heavy usage of hot water. Reduce the amount of hot water you use and it should last a long time.

I think it was a Bradford White. It was labeled as a Sear Best with a 10 year warranty. I replaced it with a Rheem Fury 5 years ago. So far it hasn't given me any problems.