How do I connect a wireless keyboard to my Mac when it is locked (i.e., cannot enter password to unlock because wireless keyboard cannot connect)?

You use a USB keyboard to log in, then connect the wireless and you are done.

If you have a Magic Keyboard just plug in the charging cable and it becomes a USB keyboard. This doesn’t work with a Magic Mouse.

My MacBook Air will not let me type in my password. The keyboard mousepad will not respond. After a couple of minutes I was promoted to restart my MacBook by holding down the off button for 10 seconds. It takes me to a page the offers three problems, I selected the third, which in “keyboard will not respond”.

I follow the prompts and type in my password, but it says Firevault will not recognize my Password. I currently do not have another keyboard to plug into my MacBook Air.

It is good practice to have a wired keyboard and mouse to use as backup when an issue with bluetooth is present. Both are very inexpensive.