If I understand you right you installed a pump and pressure tank to your existing plumbing which was at one time gravity fed.
If I have you right you have a leak somewhere in the system that didn't show up until you started using pressure. That is causing the pressure to drop. The shaking pipes may be due to the piping being not attatched to the house framing right and as the pressure is droping through the leak,they are shaking.
From here it is very hard to tell/understand the problem. This is just a wild guess, also you need a check valve to prevent the water from running backwards back into the tank. This could also B the problem. Do you have one?