Hi. The first time I did the bevel i made it 3 segments and once I created the top half of the lock " dragged" it down and tried to level the bottom part (about 9:10 in the vid) I ran into difficulty due to it having several edge loops pretty close together vertically. I went back to a previous file & did the beveling again and used one segment like you did and it made things much easier. If this was a higher poly model and you wanted a higher detail bevel would you have beveled after creating the lock top and bottom or is there a easy/another way to level the bottom? If you try and do them all at once (using the median pivot pt , scale + z + 0) it flattens the whole bottom part effectively removing the bevel. Thanks.
To your last question: you can use the Active Element as Pivot Point when leveling the bottom, that way you can for instance make the lowest Vertex active. But I don't know if that helps here...do not completely understand your question to be honest...I'd make sure all my geometry is correct before bevelling and not: bevel and then try to fix the geometry...
I'd say yes, first the geometry and then the bevel, BUT, you could also (and this is usually preferred) use a Bevel Modifier. That way you can change your geometry and the bevel will adjust. It's not the easiest Modifier, but once you get the hang of it it is extremely powerful!