at the moment it works like this:
If we like your application, we will add your steam profile ID to the moderator list, so if you come on the server one day and your name is green/blue, you've been accepted;) 

however we are soon going to change up the form to let users include their email so we can send them an email letting them know they've been accepted:)

And approximately how long does it take for an application to be reviewed?

Its normally when Nylex feels like more staff are needed

there isnt a specific review time