... for every key you have a number of modes (7) and every mode has a scale.
Yes - with a caveat. Every mode
is a scale.
The first mode in the key is Ionian and the scale intervals are W W H W W W H. Also referred to as major scale.
Yes
Other modes in the same key would start with the same note but the scale intervals would be different.
No.
In the same key you need to be focussing on exactly the same notes, not the same starting note only.
So the 2nd mode of any given Major scale is the exact same notes of that major scale but starting on the 2nd note of it.
The Key of C
C Ionian / Major
1 - 2 - 3 - 4 - 5 - 6 - 7 - 1
C - D - E - F - G - A - B - C
W - W - H - W - W - W - H
D Dorian
1 - 2 - b3 - 4 - 5 - 6 - b7 - 1
D - E - F - G - A - B - C - D
W - H - W - W - W - H - W
E Phrygian
1 - b2 - b3 - 4 - 5 - b6 - b7 - 1
E - F - G - A - B - C - D - E
H - W - W - W - H - W - W
F Lydian
1 - 2 - 3 - #4 - 5 - 6 - 7 - 1
F - G - A - B - C - D - E - F
W - W - W - H - W - W - H
G Mixolydian
1 - 2 - 3 - 4 - 5 - 6 - b7 - 1
G - A - B - C - D - E - F - G
W - W - H - W - W - W - H
A Aeolian
1 - 2 - b3 - 4 - 5 - b6 - b7 - 1
A - B - C - D - E - F - G - A
W - H - W - W - W - H - W
B Locrian
1 - b2 - b3 - 4 - b5 - b6 - b7 - 1
B - C - D - E - F - G - A - B
H - W - W - W - H - W - W
All seven modes in the 'key of C major' have been constructed using just the 7 notes (no sharps or flats) of the C Major scale and each one starts on a different note. If this was a keyboard, all seven modes are played only on the white keys.
If I pick a mode at random say dorian and use the key of C then C Ionian is my familiar friend C major scale with no sharps or flats. C dorian would be different intervals, start on C and I expect would have some sharps or flats. And the notes in the C Dorian scale would match the notes in one of the other major scales.
Yes.
Dorian is the 2nd mode. The note before C alphabetically is B. But you need to step back a whole tone, not a half (because the 2nd note of a Major scale is a whole tone higher). So you would have to use the 'B' as a flattened pitch = Bb. Therefore C Dorian is the 2nd mode of Bb Ionian / Major.
The notes in A Aolian would match the notes of C major since I understand Aolian mode is the Natural Minor scale and A being the relative minor of C.
Yes.
A Aeolian = 6th mode of C Major.
... to improvise modally over a single chord, say G, would theoretically mean knowing which major scale's notes matched which mode of G and then playing phrases from that major scale perhaps targetting the G note.
You would want to play the note G, but if your aim is to 'hear' the different flavours you would want to target the unique notes / intervals.
For instance:
Dorian is a 'minor' type of scale as it has a flattened 3rd but unlike the 'natural' minor scale (Aeolian) or the other minor mode, the Phrygian, it has a natural 6th so that would be a note to target to extract the unique Dorian juice.
Phrygian is also 'minor' in nature but it uniquely has a flattened 2nd so you would target that note for its mysteries to be unraveled.
Lydian is a type of 'major' scale but it has a sharp 4th which is where its goodness resides so target that note.
Mixolydian is another major type - almost identical to the Ionian but with a flattened 7th. The flat 7 is a big deal in blues / blues-rock and the Mixolydian is often used in these genre types.
Aeolian is the 'natural' minor so in many ways will sound familiar. Target the flat 6th.
I have linked this several times and it is worth linking again -
... you could play licks using Em pentatonic over a G chord and would be playing G Aolian, though maybe losing some of the flavour due to losing two of the seven notes of the full G Aolian scale.
No.
G Aeolian is the 6th mode of Bb Major.
E minor pentatonic is a subset of E Aeolian.
E Aeolian is the 6th mode of G Major.
So if you play E minor pentatonic over a G Major chord you are approximating a minor type of mode that derives from the G Major scale, not a minor type of mode with root note G.
There are three such modes.
The 2nd mode of G Major is A Dorian
The 3rd mode of G Major is B Phrygian.
The 6th mode of G Major is E Aeolian.
Compare the five notes of the E minor pentatonic with the seven notes of the three minor type modes derived from the G Major scale.
Which notes are missing?
Are they key ingredients of their characters?
E minor pentatonic
E - G - A - B - D - E
A Dorian (flavour note b6 = G)
A - B - C - D - E - F# - G - A
B Phrygian (flavour note b2 = C)
B - C - D - E - F# - G - A - B
E Aeolian (flavour note b6 = C)
E - F# - G - A - B - C - D - E
The Dorian mode has its essence matched with the E minor pentatonic = the note G = the flat 6th.
Neither Phrygian nor Aeolian have theirs matched up. So for any given key, minor pentatonic is a better fit for approximating the Dorian mode rather then Phrygian or Aeolian. Indeed, in Justin's blues lead lessons he does reach a place where he introduces the Dorian flavour to blues playing by adding on notes to the minor pentatonic. (see additional post below)
Last bit assumes that minor pentatonic is formed by dropping two notes from natural minor scale.
That bit is correct - not an assumption. Just a de facto piece of theory.
And now my head is about ready to burst 
Hold on yo your hat ha ha.

How did I do. If horribly wrong and confused, please say so and I'll delete this ... as well as submitting myself for some MIB deneuralisation 
Don't delete it - we learn from these discussions.
Although a MIB neuraliser may be useful ha ha.
And then back to basic fingerpicking 
Finger picking ... and breathe!