If something is not listed on a restaurant menu, can the restaurant charge for it?

You can charge for stuff you give them. Charging for that stuff is just going to lose customers, that is super cheap.

Well sure. What if someone asks for filet mignon and your manager goes out of his/her way to make it happen. Would you give it away? No, of course not. You'd charge for it.

If they fill an order, they can charge for what you ordered.

They SHOULD quote a price before filling an off menu order, but you don't get something free by asking for special service.

Yes you can but it is a common practice to give that stuff away so you just need to let the customer know immediately what the charge is for the extra stuff. People do, however, become disproportionately angry (and cheated) if they feel that are being "nickle and dimed" and, in that case, are very likely not to come back.

Generally speaking, you don't surprise customers with charges.

If they ask for something not on the menu, you can refuse to do it. Or if you're going to charge extra for it, you need to let them know the cost up front. You don't stick them with a bill later saying $5 for extra pickles, when they would have changed their mind if they'd known up front it's $5 for extra pickles.

You need to talk with your manager about how to handle such things. Some things won't have an extra charge, some things will. And it sounds like there's already a system to handle extras for pick-up orders.

of course

Why would someone pass a law requiring that a restaurant list every possible item they might sell?

This is more of a business question than a legal question because it costs money to resolve a legal question, although the answer would be that you can't charge extra without some prior notice to the customer. Also, that would apply to the business aspect, plus the fact that you want happy customers who might be irked by extra charges even if you notify them in advance.

why are you so greedy? do what the boss tells you

As long as it in clearly marked on the menu, they can charge.

If you want to keep your customers you need to give them breathing room. Sure to an extent give the customer what they want. If they ask past a certain point then you'd have the argument to charge more. A few extra pickles doesn't warrant extra charge really... Everything else you stated probably does.