WordPress Rental Booking Setup

I’m adding a dedicated booking engine to my apartment-rental site and want it running on a clean subdomain: https://book.mysite.com/. The main site is already WordPress, so please keep everything inside that ecosystem for easy maintenance.

Core flow
Guests choose dates, see an availability calendar for each unit, and submit a booking request (no instant confirmation). The system should automatically mark the dates as “pending,” email me, and let me approve or decline in the back-end. No online payments are required at this stage; I only need the guest’s name, email, and phone during checkout.

What I need the system to do
• Live on the subdomain above while matching my current theme’s look and feel.
• Allow me to add or edit apartments, set seasonal rates, minimum stays, and blackout dates without touching code.
• Send automated confirmation or rejection emails once I act on a request.
• Offer iCal export/import so I can sync with Airbnb later.
• Load quickly and look great on mobile.

Deliverables
1. Fully configured booking system deployed to https://book.mysite.com/ and tested end-to-end.
2. Short admin guide (PDF or Loom video) showing how to approve requests, adjust pricing, and update availability.
3. One round of post-launch bug fixes.

Please let me know which plugin or custom approach you recommend, examples of similar approval-based booking setups you’ve built, and your estimated timeline.