I can't answer your question about the concrete.

As far as not having received a written warranty, look up your state laws on new construction warranties. In my state legally builders must warranty the structure of a new home for 10 years. We don't get any written warranty because it's the state law. They have to do it.

Was this build started a.while ago and and left to sit and then finished recently? Or was it replacing something that was already there before? It looks like two different pours on the foundation, which seems weird and might have some problems. What other info can you get from the builder?

Before you bought the house, didn't you have a home inspection? What did the home inspection find?

It doesn't look like a serious issue but ask the Builder.

It looks like typical production and some custom.

I see typical slab construction where the footings are poured first then the slab is poured over the top after a few other things are done.

I see a hole with a little bit of Steel showing that should be patched to protect the steel.

If it were a custom home you might find that the foundation edges are parged smooth and then colored to match the house or painted. That is not required.

from the photos, it looks like your contractor poured the new concrete over the old existing foundations. Also, it can be seen that he did not apply the proper bonding agent to co-join the two differently aged concrete sections (this is why stones are coming out). Also looking at the stones, the gravel utilized in the concrete pour is dirt cheap, and big pieces like 1-2" in size. this is bad concrete. bring up the issues to the construction company immediately. i also see cold cracks in the concrete.

Was there no professional inspection before the purchase? IMO none of the concrete work would have been acceptable.

Hire a strucutral ingineer to inspect it ASAP. Maybe some if it can be repaired but some may need to be replaced.

I doubt you can get anything from the seller unless the building condition was misrepresented or it violates the building code.

When you buy a house, the rule is Caveat emptor... let the buyer beware. Warranties would only be from manufcturers of new appliances and equipment if they were given to you.

"Big holes", LOL. You ain't seen nothin'.

What do you mean you purchased a new construction home?

What lender would give you a loan?