Nobody knows exactly when they will remove it... and even after they do it will likely be available to be added back for many years to come.
Realistically this won't be a show stopper for 5-10 years in my opinion.
I wouldn't lose sleep over sites not working that you have already developed or even worry too much about using MySQL in the short term while you get more familiar with MySQLi.
I would suggest starting to use MySQLi where possible to familiarize yourself with it and start using it for new sites moving forward. I have not gone back and updated any sites developed with mySQL and don't intend to. I am however using MySQLi whenever possible in new sites I develop with an eye on the future.