A:AnswerIt should, it is Bluetooth. The port for charging is an apple priority port, and it is on the bottom so it makes it hard to use while charging, but it looks nice.
A:AnswerYes it makes a click noise (not sure of any mouse that does not). Perhaps check in the stores to see if there is a mouse that fits your needs. Or even an internet search to see if anything is available
A:AnswerIt should work fine with a MacBook Air. The only cord needed, as long as the MacBook has a standard USB connection, is a USB-to-Lightning cable, which comes with it. Plugging it in initially pairs it with the computer. After that, the only use for the cord is to charge its battery.