I think you are using trademark and patent protection interchangeably. Ge trademark covers the name of the product - the mark that consumers use to identify the source of the goods. A patent covers the function of the product. If you are licensing the exclusive use of the trademark, then you are only being granted the right to use the name. Nothing that I have seen yet tells me that you will be able to exclude others from making a similar product using a different name.
The answer to this question is for informational purposes only and does not form an attorney-client relationship.
A trademark license can be exclusive, assuming you have all rights to the underlying goodwill. You should really discuss this with an attorney who regularly handles trademark matters.
This is not to be construed as legal advice, and I am not your attorney, A conflict check and engagement letter would necessarily be required before any retention or attorney/client privilege exists.
An exclusive license should mean exclusive to the product. The "all other products" license does not seem to be part of the product or trademark licensed. As you can imagine, these rights depend on your terms and you need an experienced counsel to help you navigate these issues before something bad happens.
You need to get the services of a counsel before you unduly limit your rights.
This is not a legal advice as I do not have an attorney-client privilege with you. You should retain a lawyer before acting on any generally available advice.
This endeavor makes no sense to me. Company A owns a trademark [to brand what, you don’t say]. You want to buy a license to use that same trademark to brand a “liquid nutritional supplement / drink” that you either make or have made for your company. Company A, meanwhile, intends to sell other licenses to other companies to brand their particular products with this same trademark. So lots of different companies selling lots of different products all under the same trademark. That’s very, very unwise. Before you enter into this arrangement you need to have your own trademark attorney help you re-think this plan from the ground up – and make sure that you both look into whether Company A is really [even if accidentally] a franchisor rather than only a trademark licensor.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.