Modes of the melodic minor

Okay, so I was playing around today with the melodic minor, and I think I finally understand the so called "modes of the melodic minor".

You guys tell me if I'm right.

If we harmonize the melodic minor we get the following chords : Imin/maj7/ II min7/ bIII maj7#5/ IV7#11/ V 7#5 / VI -7b5 / and VII 7#9.

So yeah, most songs don't use a min/maj 7 chord, and also the maj7#5 is a bit hard to find, but all the other chords are used commonly in jazz.

So, if a song uses the F7 chord, then I could play the C minor melodic scale over that chord ( but using phrases that go to F) and I would be playing in Lydian b5?

I'm looking at this the same way I look at normal modes: If someone is playing an F major chord then I can make that chord sound like either the I ( play F major scale), the IV ( play C major scale) or the V ( playing Bb major scale). If I'm playing an F minor chord I can make that chord sound like the II ( Eb major scale), the III ( Db major scale) or the VI ( Ab major scale, F minor whatevs)

So if I'm making it sound like the I then I'm playing Aeolian, II is Dorian... and so on and so forth.

So for the modes of the melodic minor I do the same thing but instead of doing it with the major scale I do it with the minor melodic scales...

So if an F is being played I can make that sound like the IV ( of the mel. min) by playing C minor Melodic Scale, the V by playing Bb mel. min or the VII by playing Gb mel.min and the bIII by playing D mel.min.

or F minor : make it sound like the II by playing Eb mel. min or the VI by playing Ab mel. min

So... I'm pretty sure I understand that, because I'm pretty sure its the same concept as the normal modes but just using the mel. min instead of the major scale.

The ONLY thing I'm missing is the names of the modes... So, uh, care to help me out ?

Hello, btw, been a while since I posted here, xD