Is bootcamp free?

bootcamp are a collection of 2 things

1. a tool to partition a part of ones harddisk to have windows installed on it and generate a usb stick with the drivers for the mac hardware
2. a bootloader which choose one on is to launch windows or macos when the computer starts

when one has used 1. then one needs an windows ios (install file for windows) when one has installed windows one needs to activate it using the windows license one purchased from microsoft, that bonds with the hardware of your mac, as it would with the hardware of any other native windows computer.

Boot Camp is included as part of the Operating System so yes Boot Camp is free, Of course you have to buy Windows.

You don't install Boot Camp. You use Boot Camp Assistant to install Windows. Here are the instructions: Boot Camp - Official Apple Support