Can I use a trademark/ name of a brand if I'm using their product in my product?

No way. You can list the product in the recipe/ingredient list, as long as you take care to disaffiliate your company from the rightsholder of this famous product and give them credit for owning the trademark, but if you use their trademark in your advertising, consumers would likely be confused about the source of your product, and that constitutes infringement.

Essentially you can't do anything that would make their customers mistakenly believe that your chocolate product is made by them, and by the same token, you can't make your customers mistakenly believe that your product is affilated with the famous Pieces company's product. It's "brand fraud" on the consumers, and it would give them grounds for a lawsuit.

You can ask them for permission, but I'd be very surprised if they allowed it. Such a use would not ony infringe and wrongfully trade on their mark, but it would "dilute" their mark by using it with as product not their own.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

As noted, nope. In fact, I think you will create a dispute with the other company if you even include the name of their product in your product's ingredient list. That use of their trademark may, or may not, be lawful but the other company can, and likely would, make your life miserable while the issue is being sorted -- which I would do were I counsel for the other company.

This is a very risky proposition. The others have correctly highlight trademark law and trademark infringement as a real concern for your operation. While there is a trademark doctrine in the US, known as "nominative use", which essentially states that one can mention a trademark as a reference to describe the other product, or to compare it to one's own, it likely does not apply here. In this instance you are not comparing and contrasting. Rather you are "incorporating" the other product. This could easily mislead a potential consumer into thinking that your chocolate product is actually that of "xyz", which is exactly the type of outcome that trademark is designed to prevent. ln addition, there may be other property rights at play that you might run afoul of.