Hot water tank issue (rust or other buildup?)
That's as good an excuse as any for buying an endoscope.  I've wanted one for a while.
You did not say if you have hard or soft water.  That matters.
I think your tank is too far gone.  Tanks that do not get anode rod replacements are typically good for 8-15 years depending on usage.  Tanks that do can go from 15-25 years that has been my experience.  Your tank has been missing an anode rod for a long time now.
If you have hard water you should be periodically draining sediments.  If you have very hard water you should replace the dip tube with a curved dip tube.  This allows the tank to be drained then all of the sediments to be expelled.  If you don't do this then they build up on the bottom and cause the bottom of the tank to overheat which damages the glass and causes the tank to start rusting.
The tank is steel with vitreous glass bonded to the inside.  The glass does not perfectly cover all the steel in the tank which is why there's an anode rod.
If you have copper pipe there should be dielectric fittings used.
The hotter the temp you keep the water heater the faster it will corrode.