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.

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.

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.

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.