new heat pump runs all the time with very short breaks off.

I have recently had a Goodman Amana GSH 130241CB installed. Right away the installer had problems getting it up and running. Told it was a piston?
Also Fan on gas furnace was turned to high speed as no air was coming out of the vents. Heat pump comes on for a few minutes off of a couple minutes and on again continuous like this. Installer told me that heat pumps run 23 hours of a 24hour period. I had a heat pump previous to this and it was not the case. Between the heat pump and coil and furnace fan the noise is a kin to a train running through the house. Im finding the constant noise very hard to deal with. There is a beeping noise also near the end of the cycle that I was told is the coil and is normal. I have shut the whole system down as I cant deal with the noise. The back up gas furnace that Ive had for years is now not running like it should. It is suposed to start up heat cycle for a couple minutes then fan comes on, run together for 10 minutes and then heat shuts down and fan continues to blow for 1 more minutes before shutting down. This happens about three times an hour with the temperature at 8- 10c degrees out side. Now the furnace is on a pattern of 4minutes on. 18 minutes off and so on. The fan runs from the start to end of 4 minutes. It blows cold air to start and just starts to warm when it shuts down. The noise is way less with just the back up heat on. Also heat pump is sitting in a big puddle of water from the pump when it is running. I hope this makes sense. I am very frustrated with the whole thing.