@Blaise-and-Kami0 I don't think you understand how pricing works on Airbnb. Guests don't make an offer- you set your pricing on your calendar, and guest see that price and can decide to book it or not. You can't ask for a different price than you have listed when a guest makes a booking request.
If someone sends an Inquiry message, the dates remain open if you pre-approve it, until the guest books, or not. If you approve a Booking Request in the meantime, and Approve it, the Request takes precedence over the Inquiry. If you approve a Booking Request, the dates are blocked for that guest. If the guest fails to follow through with the payment, the dates will open again.