Should the magnesium rod be removed from a water heater if a softener is used?

The "bouncing around" that sounds like particles inside your heater is the expansion or contraction of the copper piped inside your heater. If you go to a local plumbing & heating shop, many have a "cut out" of the inside of a water heater. That may give you an idea of what's going on, as well as asking the dealer about the clicks & ticks.....

Likely the sound you hear is "bumping"; boiling in debris on the bottom of the heater. A steam bubble forms in the debris then collapses. The debris provides an insulating layer to prevent hot water from rising naturally by convection. Flushing the heater should reduce the problem. There is a valve at the bottom of the tank for flushing . The heater information probably recommends occasional flushing. I turn down the thermostat , connect a hose to the bottom valve , run it outside and open the valve for a minute.

Safe levels of drinking water are supposedly between 6 and 8.5 PH. Ideally you would want between 7 and 7.5, which is almost completely neutral, not being strongly alkaline or acidic. If the PH is within these ranges, it should greatly reduce the amount of wear and tear on your plumbing system.

The water softener may be releasing too much salt into the system which is making the water be too alkaline. Alkaline water can act as an electrolyte and form a low grade battery when it reacts with the magnesium anode. Removing the anode may stop the reaction, but could also shorten the lifespan of the tank. The anode may need to be replaced on a regular basis to prevent the tank from corrosion.

The PH of the water needs to be determined to see what adjustments, if any need to be made to the softener. It most likely is way too high, which is causing problems with your tank. I also suggest that you also inspect the anode to see what state it is in. It most likely will need to be replaced.