I just have a few questions about modes, I think I am getting a grasp on what they are but I just want to be sure.

Question 1.
I have been studying a lot of different websites and YT videos trying to learn and understand modes. And one thing I have learned/heard is that apparently playing modes is the same as playing notes of a parent scale (C Major for example) over a each of the (Parent) C major chords. So what I am asking is if I play the notes of the C major scale, using F as the tonic/root note, and play this over an F major chord, then am I playing F Lydian? This sounds very basic but is it correct? This question is not only referring to the lydian but mode but all of them. For example playing the D Dorian mode scale shape (C major scale w/ D root note) over a Dm chord then that is D dorian, and so on..

Question 2.
Would it be considered "musically correct" if I play a C major chord progression (C, F, G, C [basic, I know]) and use the correct lydian scale over each chord? What I mean by this is if I play the C Lydian scale over the C chord, F lydian over the F chord, G Lydian over the G Chord, and so on... would this be considered a lydian progression/and or would it be the correct thing to do to create a Lydian sound?

(I know the only modes and keys that I really talk about in this are C major and the lydian mode but that is just for the sake of easiness)

As always, I'm sure I'm completely wrong in my thoughts and that is why i am asking here.

Any help would be appreciated, Cheers!
Weast? What kind of compass are you reading lad?