What you have sounds like the pump is acting up to me. Have you looked at the pump?

The bladder may have failed or the air chamber is empty. This situation usually causes the pump to come on over and over. Some newer pressure tanks have a nozzle to fill the air chamber to a desired pressure.
You also may have an air bleeding valve somewhere on the line. This is the likely culprit. It allows accumulated air in the system to bleed out without losing water. It is a small round metal thing with a cap that looks like a bike tire cap. Sometimes this cap is too tight and if loosened air will start to escape. If needed try to take the cap off and press the relief valve as if you were taking air out of a tire. If air does escape when you do this the valve itself should be replaced.

what if you went under the house and somebody else turned on the water? Would you than be able to tell if it is the pump or the water line ? Water jackets cure hammering pipes- but it seems it might be in the pumping system as was said.

Can you get under there and look around ? Is there a crawl space under the house ?

Find the problem ,than find out how to fix that problem .

Problem is that after the plumber replaced it, it now "whistles" instead of jackhammers I needed to tape a small but heavy object on the "arm" that lifts up the toilet plunger to keep the whistle sound from happening. Traded one problem for the other.

Plumber says all problem were due to pressure valve, which he replaced. He says the pressure was the same as on the street (very high) and that its bad for the pipes and fixtures and cause noice and later whistling from the toilet when water was turned on elsewhere. Hopefull my experience helps someone else in the future.