Can one app read text field(s) of other apps?
A keyboard can do this - that's how a keyboard works, after all. Not only that, but for some scripts, what you describe is the most common way to enter text. For example, in Japanese, one enters む by typing "mu" (the Latin characters representing the same sound).

You can't do it with a normal app without rooting. Anything else would be a big security flaw.