Transits through airports in countries that are on the list of bans for entry into the US count as physical presence there, so no, a non-exempt non-US citizen cannot currently travel to the US via Frankfurt or any other airport in the Schengen Area (and other countries similarly banned).
The US Embassy in the Hague wrote:
Travelers with a U.S. #visa or ...
The only thing that matters is the IATA database and this is what they have to say:
This does not apply to:
nationals and residents of Andorra and Spain;
passengers in transit for less than 24 hours.
So you are indeed exempt from all COVID regulations if you leave in less than 24 hours.
If you have a single booking with KLM, or any airline, you will have to pick up your baggage at the baggage claim of the final airport of that booking, which for your upcoming journey is Warsaw. This means that the airline will arrange for each airport along the way to transfer your baggage to the next flight of your booking.
Conversely, if your journey ...
I think this will be fine assuming you have the proper documents for entry (the German long-term "D" visa is listed as an exception allowing you to enter / transit through the Netherlands according to IATA TravelCentre) and regarding Covid regulations (I haven't checked these for your specific situation).
I've arrived at Schiphol (as my final ...