How to choose the right capacitor for Harbor Freight AC Welder to DC Welder conversion?

I'm watching this series of videos about improving a cheap harbor freight welder. Right now the step is converting the AC to DC. It seems like the guy is just using whatever components he has laying around or that are the cheapest but I want to make sure to get the most power as possible.

Here's the AC to DC conversion video: 


Here's a link to the Harbor Freight page with the welder specifications:


It says on the specifications page that the open circuit voltage is 26 volts, does that probably mean that that's the max output voltage at which the welder operates?

Anyways, here are my questions:

1.Can a capacitor be fully charged by a lower voltage than it's rated for? For example, the modification in the video uses a 50V capacitor to store charge from the transformer of the welder, which I'm assuming is a 26 volt or less source. Will it still reach it's 46,000 microfarad charge storage potential or does the charge storage potential vary based on the charging voltage? In which case could the capacitor store more charge at a higher voltage, a lower voltage, or wouldn't it make a difference?

2.For the rectifier, assuming the max output of the welder is 120 amps at 26 volts, I am thinking that the guy in the video should have used a rectifier rated for at least 120 amps, probably somewhat more than that to be safe. But instead he is using a rectifier rated only for 100 amps at 1600 volts.

That's it. Basically what do you think of the modification. Are those components in the video adequate, the rectifier and the capacitor, or if doing this modification would you have selected different perhaps higher rated components.

I have a habit of thinking that I'm too smart to follow instructions exactly and then wondering why things go horribly wrong when projects, recipes, etc. don't turn out.

1.) Yes. It will charge fully.

2.) Big rectifiers aren't very expensive. Go large....

Thank you Steve! Short and sweet.

It might explain why it got so hot in the videos.