The Glyph's caster
Who is considered to be the caster of the spell upon triggering?
The original caster of the glyph spell, who is also the one who casts the spell into the glyph.
Is it the original caster
Yes
or does the spell glyph "recast" the spell that was stored in it?
The stored spell was cast in the creation of this particular glyph. What the glyph is doing is storing the magical effects until the glyph is triggered.
Duration: Until dispelled or triggered
The caster casts the spell. The glyph is a discrete magical effect that allows the stored spell's magical effect to be delayed until the trigger.
You can store a prepared spell of 3rd level or lower in the glyph by casting it as part of creating the glyph. (SRD V 5.1, p. 149-150)
The you here is the caster of the glyph spell.
What is a spell?
A spell is a discrete magical effect. (PHB. Ch 10, p. 201)
A caster is a who. A spell -- like the magical effect created when you cast Glyph of Warding -- is a what.
You decide what triggers the glyph when you cast the spell. {snip} You can further refine the trigger so the spell activates only under certain circumstances ...
A similar mechanic to assess the spell DC, slot level, spell attack bonus, etc (the whole magical effect) cast into the glyph is the ring of spell storing. It to stores the effects of a spell cast into it until a later time. There are other mechanical differences between the glyph and that ring that make further comparison moot, such as being able to store multiple spells and portability.
- As @NickBrown kindly noted: "caster" is the glyph's caster as he/she existed at the time of casting the spell into the glyph. Level ups, curses, magic items, and even death which have occurred since then should not affect the power of the spell when finally triggered.
Your cases:
• If you cast dissonant whispers into the spell glyph and creature(s)
trigger it and fail their saves, do they run from the person who cast
the spell into the glyph or from the glyph itself?
The major benefit of the glyph of warding spell is that you don't have to be there when the stored magical effect goes off. In this case, the point of origin of the spell's magical effect is a sufficient point of origin for a direction to run from. Since the rules don't try to specify all edge cases, make a common sense ruling. If the caster happens to be in visual range when the glyph is triggered, it would certainly be sensible for the caster's location to be where the target runs from.
• If the stored spell is major image, does the original caster get to
move and control the created image after it is triggered as if they
had cast it normally? Or would they be unable to because the glyph is
effectively the caster now?
Neither, unless the caster is within range to do all of that.
As long as you are within range of the illusion, you can use your action to cause the image to move to any other spot within range.
If you aren't in range (you being whomever casts the major image) you can't use that feature of that spell since you don't meet that requirement of that spell.
Once again, the major benefit to the glyph of warding spell is that the caster need not be there when the effect is triggered. If the caster takes advantage of that benefit, then for spells where some micro-management of the effect is needed that micromanagement sub feature can be lost as a cost of the benefit of having a "fire and forget" spell ready to trigger. As above, use a common sense ruling. It is within reason to believe that a third level spell might not be all things to all casters nor perfectly compatible with all other spells.
The above adjustment in the stored spell's magical effect is consistent with a spell's duration no longer being selectable for a spell with the concentration requirement. Usually, when a spell caster has a concentration feature in a spell, the caster can stop the spell before the full duration. In the glyph case, it runs for the full duration since the caster is not there to micromanage it. It makes sense that if you aren't there (within range) to micromanage the illusion, you can't micromanage the illusion. The glyph is something you are storing the spell's magical effect in; it is not described as a sentient being.
The matter of concentration
If the spell requires concentration, it lasts until the end of its full duration.
That a spell requiring concentration can be cast into a glyph is addressed here. The default to "full duration" addresses both
- That nothing can hit a glyph to break concentration (a glyph has
no HP)
- The spell's duration can't be selectively shortened.
The spell in the glyph is preloaded to do one thing. As @NautArch put it, this feature of the spell 'unloads' the concentration requirements from the caster but does not change who cast the spell.
