Hey there, it's my first time flying with a connection and I need this answering!

I'm flying from Manchester, UK to South Carolina with a layover in Atlanta. I have all my flights booked on the same itinerary with the same ticket number. I'm flying with KLM, but operated by Delta Airlines.

Question 1: Will I have to recheck my luggage in Atlanta? Considering I'm coming from the UK.

Question 2: Since I'm flying with the same airline on the same ticket number, I assume baggage fees are the same as when I left the UK when I connect? (i.e one free hold baggage and one hand baggage)

Thanks!