"Now the electrician has returned and changed the cable to the GFCI receptacle in the basement from a 14 AWG to a 12 AWG cable (which is correct for a 20 amp circuit), removed the potential fire hazard, but piggy-backed the cable to an existing 20 amp circuit that serves the counter-top receptacles, yet another code violation. Is it now that the receptacles in the kitchen started failing?"

To answer the above quote: He piggy-backed the GFI to an existing 20amp circuit that serves a receptable for my microwave and toaster. These all work. The receptacles near my countertop do not work which are NOT on the same circuit or they would be working, right? This is where the concern is with a possible hazard.
I am having a friend of mine's husband who owns his own electrical business come out and check it. It won't be free but it will be done right. I don't think the original electrician was planning on ever coming back or returning the 15amp tandem breaker he took with him. I think the only reason is because he left an expensive jacket here! I'm waiting for him to call to let me know when he is coming. IDIOT!

It is important that you know when the kitchen counters failed.

For example, they may have damaged more than the one breaker they told you about.

I would tell the waterproofing company that they will be receiving the bill for the repairs completed by the new contractor. I would also tell them that the electrician they sent, did not follow electrical codes correctly.