Bion,
You have two very separate issues.
The lights flash with the pump load means that there is a bad connection. It is probably between the house bank and the panel if all the lights are affected.
The short cycling means that there is a leak. That leak can be anywhere. If you are not finding a drip or a puddle, then it is internal either to the pump (Just because it is new does not mean it is good) or, if you have a valve that allows you to fill the potable tank when connected to city water that can easily be it. Check to see if that valve is solidly closed, If it is a 1/4 turn ball valve and was not cleared correctly, it may have had water left in it that froze and cracked part of it.
Matt