I want to know if it's possible to use Node.js in place of MySQL.
No, it's not. Node.js and MySQL are completely different things.
As you can see, one is a database (MySQL), the other one isn't.
You can however use MySQL and Node.js together, or you can use a plethora of other database systems in combination with Node.
No and yes.
Yes because there's something being cooked right now called tingodb which is a DB and capable of replacing MySQL.