"Yes[1,3] and yes[2]. Have you been in a cave for the past two years?"
Yes, the NSA can monitor specific targets. Do they monitor all Internet traffic worldwide? No, such a task is absurd and technically impossible. However I have learned that people's opinions about the NSA are faith-based, and not open to reasoned arguments.
Sorry, but "absurd" - yes it is absurd - THAT THEY DO IT.
And, also: "technically impossible" - also: NOPE. Technically possible! In fact so technically possible it is a done deal. You cannot turn off the NSA, for to do so would be to turn off the entire Internet.. we get the copy, NSA gets the originals.