Had to do manual loadsheets quite often and in the end nearly every flight. Nowadays all loadsheets are done by the flightcrew but we do not have any provision to do a full manual loadsheets, we just do an abbreviated one using our EFB. Good thing about that is that the data from the loadsheet is transferred into the performance program and vice versa.
But i guess it is much easier to do load and trimsheets for a 737 than widebodies.
There was no formal requirement to do training loadsheets to keep current. We were once trained and then it was expected that we were able to do it. It is actually quite easy and can be done in 5 minutes or less if you do it often enough. And yes, even our captains could do it
Although some cheated and used an excel spreadsheet on their PDAs.