In fact if you are talking about the C Ionian and the A Aeolian modes having the same notes, you are correct. Also the D Dorian has the same notes, the E Phrygian has the same notes, the F Lydian has the same notes, the G Mixolydian has the same notes and the B Locrian also has the same notes. They all use the same notes as the C major scale but the difference is, they all start on different notes, or degrees of the C scale. Do you realize this? It is very important. Every Ionian scale you can think of has different relative modes. Do you know the intervals of the major scale? Do you know what a whole step and a half step is on your fingerboard? These are important things to know when you are getting into modes. They go hand in hand. They change with each progressing mode in the order that I delineated in my first post. I don't want to explain if you already know the basic building blocks of the modes, but will if you don't.
Not exactly. As I alluded to in part A of this post, Each major scale has it's own relative modes and they don't usually mix very well with each other. Let me try to give an explanation of what you don't seem to be getting. You can play in the C phrygian scale but C Phrygian is not relative to the key of C major, so you will be using a different set of notes...not the notes of the C major scale. If you play the notes of the C Phrygian mode, you will be using the notes of the Ab major scale but starting on the third note of that scale, which happens to be C. then the next note will be Db then Eb then F and so on.
Playing a C phrygian scale then moving it up to G relative to Em doesn't make any sense. In the key of G, E is the relative minor and E starts the relative Aeolian mode to G. In G the relative Phrygian mode would be B Phrygian, B is the third degree/note of the G scale and starting on that note and playing the same notes as the G major scale gives you the B Phrygian mode. B C D E F# G A. This brings me back to the intervals of the modes/scales. The Phrygian mode always goes Half step, whole step, whole step, whole step, half step, whole step, whole step from B back to B in this case.
Try finding songs that use the phrygian mode for the melody. The Simpson's Theme is one. Listen to how that sounds to get an idea of how the notes work together.