F121A engine serial number: F = Flint, MI engine plant
12 = December
1 - 1st day of the month
A = automobile 235 engine with manual transmission
All car 235 engines from 1956 onwards had hydraulic lifters.
"Secondly, when setting the rocker arm clearance for hydraulic lifters, does it need to be done hot?"
Yes, "normalize the engine" and adjust the hydraulic lifters as per Shop Manual.