No, hags enjoy no special protection from death, on the Material Plane or elsewhere. As you mentioned in your question, demons, devils, and yugoloths all have a paragraph in their description that explains how they cannot be killed on the Material Plane. However, no such ability is given for either the fiend type in general, hags in general, or night hags specifically. Interestingly, despite their long association with demons, this means that Succubi/Incubi also now die when killed.
No
To open, lets look at a sample of the rules that say you cannot permanently kill such a creature outside of their home plane...
The only way to truly destroy a demon is to seek it in the Abyss and kill it there.
MM 51
Devils that die in the Nine Hells are destroyed forever
MM 67
Only on its native plane can a yugoloth be destroyed permanently
MM 311
Of note: Angels in the 5E MM do NOT have this protection. Weird as it may seem, it is actually easier to kill a Celestial than it is to kill a Fiend.
The nature of Astral Projection is that your Physical Body and your Astral Body are separated. Your Physical Body is left behind on your 'Home' Plane while your spirit goes walkabout.
Bringing Fiends and Celestials to the Prime doesn't work like that. When you summon one, it isn't just their spirit you are summoning while their true body is left behind on their home plane, you actually summon them.
The descriptive text for Demons on MM 50 says
Wherever they wander across the Abyss, demons search for portals to other planes.
The descriptive text for Devils on MM 66 says
Devils are confined to the Lower Planes, but they can travel beyond those planes by way of portals or powerful summoning magic.
In both of these cases, it is explicitly mentioning 'portals' as a way that Fiends find their way to the Prime. Portals are a way to physically move from place to place, not a way to send your spirit somewhere without your body tagging along.
Gate, in essence, is a portal that you create between where you are and anywhere else that can suck something through if you know their True Name.
Thus, a Demon who found a Portal to the Prime Material Plane and a Demon who was called to you through a Gate both, effectively, arrived on the Prime in the same way. They are both entirely and physically there. And because they are not on their Home Plane...they cannot be permanently killed.
Simply put...Astral Projection is the exception to interplanar travel rules - it is not the general rule. Plane Shift, which physically moves you to another plane, is only 7th level--compared to the 9th level Astral Projection. Astral Projection is special because it gives mortals the same degree of insurance when plane-hopping that Fiends and some Celestials enjoy naturally.
Just as a cautionary note, though: if you are Astrally Projecting, watch out for 'Silver Swords' (most commonly wielded by the Githyanki). Those can still kill you for real.
To sum up:
tl;dr:
The books say that a Fiend cannot be permanently killed on a plane other than their home plane. How they left their home plane doesn't matter.
Astral Projection is an incredibly powerful spell because it lets an Adventurer mimic that same feature via magic.
Best Answer
It reforms in the Abyss
Nothing states that a shadow demon itself cannot reform, only that it is created by the failure of another demon to reform.
(Monster Manual 54)
However it is still a demon and when a demon dies...
(Monster Manual 52)
A shadow demon remains both a fiend and a demon so this rule applies.
If the demon is still prevented from reforming (such as by the same effect as the original demon), the essence of the shadow demon could become a new shadow demon or not since a demon that can reform only "sometimes" assumes the form of a shadow demon.