Messenger is an app???

If you mean the Facebook Messenger app, yes you will need to install that from the App Store.

Download apps and games on your iPhone or iPad - Apple Support

Facebook Messenger is free but other apps and games may cost money or require subscriptions.

Not at all, that should already be installed on your phone go to the App Store

yes this is a app from apple install from itunes

[Link Edited by Moderator]