@Abrasha-and-Maria0. Let's see if I can clear some things up for you!
An Inquiry will not block your dates unless you choose to block them after sending a Pre-Approval or Special Offer. And, yes, the dates must be available for the guest to use the Contact Host link to send you an Inquiry.
A Reservation Request, on the other hand, does block your dates since with a request Airbnb places an authorization hold on the guest's payment method pending your accepting or declining the reservation. Since authorizations for payment cannot be held indefinitely, Airbnb requires that hosts accept or decline within 24 hours.
From what you describe, the other host sent you a Reservation Request, not an Inquiry.
Here is the difference between the two:
Inquiry: Guests can send Inquries to many hosts at the same time. The guests are essentially window shopping and are asking questions without a commitment to reserve. Since they are allowed to send multiple Inquiries at the same time, they will receive responses from several hosts, some with a Pre-Approval or Special Offer. The Pre-Approvals are simply an invitation to proceed with a booking providing they respond within 24 hours and the host has not accepted a Reservation Request or Instant Booking in the meantime. Simply responding to the Inquiry is all you have to do.
Reservation Request: These come from guests who are ready to commit to a reservation. As mentioned before, Airbnb places an authorization hold to be sure they can pay for the requested reservation. These take priority over Inquiries and will automatically block the dates on your calendar until you accept or decline the booking.
There is an excellent Community Help Guide that describes the difference between an Inquiry and Reservation Request. Here it is:
https://community.withairbnb.com/t5/Hosting/Reservation-Inquiry-or-Request-What-s-the-Difference-A-C...
If you have more questions, please ask!
Clare