Can I reuse chopped onions?

If you're operating a hot dog stand, I'm going to guess that you'll want to follow your local health codes. There's a very good chance that it'd be a violation.

In most areas, it wouldn't be anything to stop you from using it for your own meals, so long as you didn't serve it to the public. (and you might have to transfer it to a different container, so you keep the public & personal stuff seperate). So long as they've been kept chilled through the day, I'd be inclined to use them in some sort of cooked dish for dinner. At worst, you get sick, but you don't get the public sick.

This is a good thread to read about storage time for onions after they've been cut.

There are also some ways to attempt to keep an onion fresh.

If you're cutting your onions to serve then Joe is correct in stating that you'll want to adhere to local health codes and possibly even consider cutting your onions to order or only cutting a small amount and adding to it as needed- any good customer would prefer a fresh cut onion to an off, cut up cup of them anyway, right?

It's also prudent to remember that in nearly all cases you cannot see whether or not a food has gone bad entirely, but since you stated there is a watery liquid in the bottom of your onions it sounds like there are some visual indicators.

Just remember: If in doubt- throw it out (especially when you're serving it to the public)!

Most cut vegetables have a shelf life of 24 hours, I've worked in restaurants were they "extended" the shelf life, but a health inspector would look for a same day sticker to indicate that those onions are not left over. If you are finding yourself overwhelmed with the amount of prep needed and are over prepping to compensate and stay ahead, pre-prep your onions. You can do this by having a cambro of peeled onions (or complete whatever primary or secondary steps you follow before reaching your final product) and then cut only what is needed for that day. If you're having trouble figuring out how much onion you need for the day weigh the amount of onions you prepped before and after service, and see how much was used.

Use 3-4 smaller containers so you are not opening and closing it multiple times and bringing the onions out of the cooler multiple times. And you are not mixing old onions with new.