The 5th is usually the first note sacrificed in extended Chords. For example (but this is not always the case) The root and third define the chord and the 7th, 9th etc embellish the chord so the 5th can be omitted. But this isn’t written in stone so you will find inverted chords that leave off the Root but the 3rd being it major or minor always stay unless covered by another instrument.
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To me there is no difference. People use various notations to describe the same chord.
I like to keep it simple: an Em9 implies the presence of the b7, so I leave it out of the chord name. The same for (m)11 and (m)13 chords.
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On question 1 I answered G7b5 and then wrestled with myself over why G7#11 makes more sense (besides the fact this is obviously an extension lesson). What I arrived at:
A G7 chord implies the natural 5th, D. You wouldn’t have D and Db in the same chord, and G-B-Db isn’t any kind of triad we’ve learned. I think I was mistaking this for “half-diminished” so I may need to review the 7 stuff again (or just get some caffeine). I even made myself test this my tuning my top string down to D and playing it open with the chord, with and without that #11. I feel much better!
Welcome to the Community @Swagnasty
The 5th may be implied but is often the first note that is omitted when an extended chord is reduced in size. Be aware that you will often find grips that have no 5th … and some that have no root.
Essentials are the 3rd and the b7th.
Others may be removed.
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Nailed it. Must have a good teacher 
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A stupid question probably but I would like to clarify it. I know that min7 chords are consisted of R, 3b, 5 and 7b, and I haven’t thought much about it before, but I guess we are determining the quality of each chord relative to the major scale root (in Example 2. that is E, so relative to E major)? Because after determining the root and 3b which would mean we have an Emin, we come to a D, which in Emin scale is a natural 7, not a 7b… which would imply that we always use major scale for determining the qualities right, regardless if the 3rd is a flat (minor) or not. Just a small thing but I feel it is important to clarify, at least for me. Thanks