I'm not sure how bacteria would be any more or less present because of a spent anode rod. They sacrifice themselves to keep your water from eating the tank.

They cost around $10-$50 depending on make and model. Plumber will probably charge you an hour's labor. + / - $100

It's an EASY job if you have a wrench.

No no suphur smell is not from hot water tank its in your water.weve had same problem 20+ yrs.My hubby talked to someone they said you need to pump air in water we did.It worked awhile.We have very very hard water iron stone...He decided to drill another well.Weve been wanting a windmill we did it ,worked about 20 yrs but like 3xs a month I smell it its trying to come back.We had specialist come in tell us what we can do.My water is way hard.He couldn't believe it.

You'll probably want to use a water conditioner to remove the hardness of the water. There seems to be a lot of sulfur content in your water (which causes the rotten eggs smell).

If it is just the hot smelling, check to see what temp your water heater is set on. If it is 120 or so run up the temp to 140 and see if that doesnt help it. Had a friend with this problem and it solved his problem. Worth a try before calling in the plumber. Bacteria in tank needs killing out.