Here are some answers to your concerns:

Q: What size of hole needs to be cut? 
A: You will need to cut a 15'' x 15'' hole to place the fan before installation. Fans can be installed both inside and outside the walls.

Q: How to connect these wires inside the fan?
A: No assembly required. Complete kit includes the fan unit, the controller, corded sensor probe, and power it through an outlet.

• 12'' Exhaust Fan: Dimensions: 15 x 15 inch | Airflow: 940 CFM | ETL Listed | Speed: 1650 rpm. Our high-airflow exhaust fan can eliminate heat, humidity, unpleasant odor, and dust from rooms, buildings, and small enclosed work areas. Get ready to relax and in clean air in all your rooms.
• High Performance: 120V/60Hz, 40W. The wall exhaust fan has a premium EC motor that maximizes airflow while reducing noise and power consumption. And the fully enclosed motor has thermal protection and permanent lubrication for security and easy maintenance.
• Smart Programming: We are equipped with an intelligent controller! Not only do you have temperature and humidity triggers, but it also allows you to set up to 10 speeds that will respond to changes in them. You won't miss a thing and will always be ready to adapt! There are multiple modes, allowing you to adjust as you wish. Timer and alarm modes are available on demand.
• Rust-proof Material: The shutter exhaust fan has a rugged all-metal structure and features a powder-coated steel frame, aluminum alloy fan, and shutter, which is highly resistant to weather, liquid, and dust. It is perfectly suitable for any place you install and stays with you through the long, sultry summer!
• Plug and Play: Get ready to fly through the installation process! Our wall mount exhaust fan comes fully assembled and ready to install right out of the box. Includes 4 bolts. You're ready to go by connecting the 5.9 ft power cord. No more worrying about wiring! Works well for garages, workshops, chicken coops, sheds, attics, greenhouses, etc.