Some brief comments:

1,

I can't say I've ever heard a VI chord of any sort used on a Dorian tune, but I'd be curious to know how a simple VI-minor or VI-minor7 would sound in a Dorian context.

The natural 5 of the VIm, would clash with the minor 3rd of the Dorian and make for an overall mixolydian sound which would affect the character of the tune as the tune could have to take on a major tonaliity temporarily to compensate, which would equate to a tempotary change of mode.

In which case the tune becomes modal in two modes.

I suppose the blues thing of having an ambiguous third could be relevant, but it wouldn't really be modal anymore then either, it would be a blues.

The answer I suspect, as is often the case, is probably all to do with context.

2,

Where there is a dominant 7th in a minor key, you can't say that the music is modal so you can't really use it as an example of an exception to the rule.

The whole point of the Dominant 7th chord is that it is the quintessential Functional chord.

It can be superimposed in many different places to establish tonality and to modulate into different keys.

Therefore, when you see it employed in any context, you know you are dealing with functional harmony and not modal harmony.

3,

"Similarly, the dominant (V) chord, whether major or minor, will probably carry a minor 7th even when the 7th of the modal scale is major."


I can see that a Tune in the Lydian mode could conceivably use a dominant 7th as its V chord to help establish its tonal centre, but the problem with that would be that the Flat7 of the V chord would correspond to a natural 4th in relation to the tone centre of the tune.

This is of fundamental importance as the only thing which makes the Lydian mode different to the major scale is the sharp 4 (#11).

This is the colour note and 100% essential to any lydian composition.

To flatten it in the V chord would be to establish a clear natural major tonality.

Dominant chords are extremely powerful bombastic tools which is why they perform such a useful functional purpose, so they would shout out "This is not Lydian" at the tops of their voices for the duration of the time they were played to the significant detriment of the tunes character.

I would therefore argue that adding a dominant 7th onto chord V in a lydian tune would render it functional and not modal.