I agree on replacing the tank. I don't agree that it is corrosion from electrolysis. If it were, there would be signs of leakage where the copper piping is connected to the tank at the threaded fittings. Copper corrosion would be greenish-blue and iron would be reddish. That appears to be yellowish, such as with sulpher compounds. It appears to me that the water connections on the tank are leaking, enough to leave mineral deposits when the water evaporates, from what I would guess would be hard water, but not leaking enough to form puddles. Note that the yellow stuff heads towards the draft hood. The draft would be pulling air, and moisture, up the flue.
The PT valve is leaking as shown by the rust (iron oxide) streaks on the side of the tank. In my opinion, that is an unusual amount of corrosion for a 10 year old tank, and I suspect that it had been leaking for quite some time.
I disagree that most water heaters last 5-8 years, at least in this part of Vermont. Most are warranted against tank leaks for 6 years, some as much as 10 years. I have seen many propane (we don't have natural gas available in most of this state) water heaters that are far older, often lasting 10-20 years, and those that have leaked from manufacturing defects tend to leak in the first few years.