Flashing ROMs means Installing zipped apps? My sister and I have Galaxy S4 and a Galaxy S3. Along the time of usage we have only downloaded common apps like social apps and games. We've never downloaded any system-related apps such as those used to root a phone. Thus, both phones are not rooted.

Questions:     


Is it possible for an app (before installing) to be in the form of .zip file instead of its usual .apk file (before installing)?
(not the normal archive .zip file)
Does flashing a ROM mean putting a .zip file (with app inside it) in an external SD card, then pressing the Volume-Home-Power keys, later installing it?
Let's say I did all the steps in question 2 using the unrooted S3 and S4, will I successfully install the zipped app to the phones?
If question 3 fails, what other ways do I have to install the zip file? And I don't have access to the computer.


Those are the things that bother me. If there are things very wrong please correct me.
Android can only install .apk files (though .apk and .zip are interchangeable)
Yes, it does mean that, but you'll need a custom recovery which has the ability to flash .zip files. Note that such .zip files are not just applications packed in an archive, those .zip files are specifically designed for recovery flashing, and have specific scripts that run when they are flashed
installing custom recovery requires root
As said before, you need root to have recovery so that you could install .zip files. To achieve root access, you'll need a PC.