I am a dual national. My B-1 is on one passport, and I have a Caribbean passport and I wish to have F-1 visa. While applying to embassy for F-1 what should be said and will they cancel my B-1 on other passport? B-1 was valid 2025 though.
Everything about US immigration law applies to you as a person, not to each of your passports. When you apply for the F-1 visa, you'll be asked on the form whether you have ever visited the US and been issued a US visa. You should answer these questions honestly (fraud on a visa application can result in a lifetime ban) and report the details for your B-1 visa and previous visits as requested.
They may well cancel your B-1 visa if they issue you the F-1 (see this question), though it is possible to hold more than one US non-immigrant visa at the same time. If you do retain both visas, it is very important to enter on the right visa based on the purpose of your visit, or you may not be allowed to study. It is possible to have both visas, but it is only possible to be in the US under one status (business visitor or student) at a time. Entering the US on the B-1 visa when you plan to study will create a substantial headache that you don't want to deal with.
If your B-1 is cancelled, the cancellation shouldn't be held against you (as it would be if it was cancelled for fraud or an overstay) if you apply for a new one after you complete your studies.