Confused about modes?

[ragasaraswati]

The C note .... is this the tonal center everyone keeps talking about?

No, you chooce the tonal center. C is an example.

Next I would like to ask a very simple question. I noticed that the C note
in the above example exists in every scale relative to the mode. For example
C Dorian mode has the C note in the scale of Bd
C Phrygian mode has the C note in the scale of Ab
C Lydian mode has the C note in the scale of G
etc...

It's no wonder every exercise about modes use this as an
example to demonstrate the sounds of all the major modes.

But lest say the bass player would be holding that C note
and the guitar would strum a C major chord, we would
have to be careful which mode we select to play a melody
over this.... right?

Yes. Only major modes apply. Ionian, Lydian, Mixolydian.

So now it becomes a selection process of which mode
covers the notes in the C major chord
right?

So given this, the following modes cover all the notes in the
C major chord:

C Ionian mode, (Major)
C Dorian mode, (Minor)
C Lydian, (Major)
C Mixolydian, (Major)

However given the fact we are playing a Major chord (C major)
out of the above list only the following can be selected:

C Ionian mode, (Major)
C Lydian, (Major)
C Mixolydian, (Major)

am I seeing this right ?

Yep. The key as you can see is comparing the modes in parallel. C Ionian, D Dorian, E phrygian etc. only confuses people.