It is reasonable for the hotel to ask us to pay the deposit without a menu or exact price. If you don't pay, you won't stay, and you won't sign an agreement.

If they promised verbally at that time, you didn't record it at that time, and they didn't violate the law. I used to work in a hotel. Usually, the price (including deposit, catering dishes and drinks) and other services (including being your master of ceremonies, chasing lights, holding flowers, cakes, etc.) must be discussed with the hotel, and the engagement will be worked out in black and white.

I suggest you pay the deposit first, and then they will give you a receipt to prove that you paid the deposit, so that you won't leave without a day. Moreover, it is best to sign an agreement when paying the deposit. Most hotels have this version of the agreement, just fill it out.