your old honda takes dexron III ATF and its supposed to shift very crisp/hard. Thats how old hondas should shift. It has a shift pressure cable, adjust it as required to get the required shift characteristic. It changes the rpm and the quality of the shift too. The oil level check is done the usual way, engine running, warmed up, shifter in P.
the reason Honda say to do it at 20 seconds after shutdown is because the dipsticks are tiny and hidden deep - they do this to avoid operator injury.