@Ashrin:
You can't root an app, you can only modify Android so that apps that request root access can obtain it. ("Rooting" is just copying the file su to the phone - you can't copy a file to an app - not in that meaning of "copy to". Since you have no console from which to run the apps, you need an app like SuperUser or SuperSU to do what you'd normally be doing in, say, Linux - asking for root access from su.) An app that doesn't request root access can't tell whether the phone's been rooted or not - and it makes no difference to that app.
If you root the phone (you're not, really - see later), those apps that need root can obtain it. If you install the apps first, then root, the apps that need root can obtain it. Which one is done first is irrelevant - unless you haven't rooted the phone, install an app that requires root access and try to run it. Since you haven't yet rooted the phone, the app can't obtain root access, so it can't run.
You don't root an app, you don't root a file, you don't even root the phone, you root (in the Android sense) the operating system (the ROM). You modify the operating system so that it can grant root access to anyone ("one" includes apps) requesting it. Most modifications of *nix (Unix, Linux, BSD, etc.) include a method of obtaining root access, Android (for VERY good reasons) doesn't - which is why people "root their phones" (which usually falls into the "one of the worst ideas" column - there's almost no reason for 99,9% of people using smart phones to root them. (Almost - there are 2 or 3 sort of good reasons someone who knows almost nothing about cellphone internals might have for rooting. "My phone is rooted" isn't one of them.)