The ground staff will sign their section of the load sheet,
Not at my Airline. They don't see it or get a copy of it.
they will sign the technical log confirming the aircraft is fit to fly and it is then countersigned by the captain.
Not at my Airline. The Captain just reads, no writing/signing.
There really are no ifs or buts about this with airlines of any size
Incorrect as per examples above. ( moderately sized Airline operating both Airbus and Boeing.