Water heaters do not come with expansion tanks
. Its a good Idea to have one. Required by most US plumbing
codes for landside plumbing
I would get one from the bog box store, about a gallon size or so. less expensive and works better / longer then the accumulators sold in marine
You don't need an accumulator with a VSD pump, but it works as a thermo expansion tank too
Its more an issue in boats where the hot water is being heated by the cooling
water. Lots of temperature swings.
Note: on your first question, the start stop, could be caused by a slow leak somewhere in the system, or leak back to the suction side of the pump.