There is no FAA limit on constructing homemade airband receivers.

You can also construct transceivers. As long as you do not sell a transmitter you are allowed to make and operate up to 5 of them.

The exemptions covering low power transmitters are covered in Part 15 of Title 47 in FCC regulations.

The maximum unlicensed radiated output power for airband is 500 μV/m @ 3 m. Typical commercial airband handheld transmitters go up to about 1 Watt and base stations up to 50 Watts. For your purposes a 1 Watt transceiver would probably be reasonable.