Do I need to get an engineer for badly poured conctrete basement floor?
If it would ease your mind, hire an engineer to look into it. Of course, having built a house on top of it, it's a bit late to do over.

However - if this is a typical New England house, the floor (that looks horrible, yes) is not holding up your house. The footings and foundation walls, which are normally poured before the basement floor, are the support structure. The basement floor is just a floor.

Water and concrete have an interesting relationship. Excess water in the mix does make the concrete weaker. Once the initial set has taken place, there is no such thing as too much water - one method for making high quality concrete runways is to flood them for a month after they are poured. Wet-curing concrete makes it stronger.

In your case, I suspect what you have is a little bit excess water on the surface before the initial set was complete, and a lot of letting the concrete freeze before it's cured. The surface damage is called "spalling" if you want to look it up. That does not say very nice things about your general contractor or your concrete sub-contractor, in my opinion - they should either choose to work in a weather window, or be prepared to protect and heat the concrete for a proper cure if working in the winter. The document linked above from the Portland Cement association specifies that fresh concrete should be maintained at or above 50F until it is cured (and curing takes longer at that temperature than the "standard" 73F.) Unless you are planning to put a machine shop in your basement (a good thing to have, IMHO) a self-levelling top surface will probably be adequate for most normal household uses. But you almost certainly don't have the floor you should have.