[...] I certainly would use this over lead free solder with all the problems that could bring.
While nobody is ever going to claim that lead-free is superior to leaded solder, that video is useless. He's comparing a vaguely decent leaded solder to crappy Chinese lead-free. And as it happens, people who've compared tons of different solders, both leaded and lead-free, both Chinese and high quality, find that Chinese solder usually sucks, no matter what its (claimed) composition. So in that video, the problems he's attributing to lead-free are actually just the issues with Chinese solder. (That and questionable technique.)
If one compares high-quality lead-free to high-quality leaded, the lead-free is really only minimally harder to work with, aside from needing a few degrees higher temperature.
As for old solder, I have a roll of Kester bought sometime around 1990. It went unused from probably 1995-2015, and in that time the outer layers tarnished a bit. This didn't seem to obviously affect its performance, though, and one option was simply to use a tissue with IPA to clean off the surface a bit before use. Inner layers are shiny like new, and perform great.