The descriptions of the hag eye and soul bag in the MM specifically reference the hags that created the items when talking about who uses the items.
Hag eye:
A hag in the coven can take an action to see what the hag eye sees if the hag eye is on the same plane of existence.
Soul bag:
A soul bag can hold only one evil soul at a time, and only the night hag who crafted the bag can catch a soul with it.
So those items are clearly limited to the hags. But the heartstone, I think, is somewhat open to interpretation.
Heartstone:
This lustrous black gem allows a night hag to become ethereal while it is in her possession. The touch of a heartstone also cures any disease.
From this, it looks like etherealness is only usable by hags, but curing diseases could theoretically work for all.
Jeremy Crawford has commented on this saying it's meant to work only for hags, but DMs can rule otherwise.
If you're looking for a way to use the stone for curing diseases, I'd refer to the 3.5e Wiki, where a heartstone is described as follows:
All night hags carry a periapt known as a heartstone, which instantly cures any disease contracted by the holder. In addition, a heartstone provides a +2 resistance bonus on all saving throws (this bonus is included in the statistics block). A night hag that loses this charm can no longer use etherealness until it can manufacture another (which takes one month). Creatures other than the hag can benefit from the heartstone’s powers, but the periapt shatters after ten uses (any disease cured or saving throw affected counts as a use) and it does not bestow etherealness to a bearer that is not a night hag. If sold, an intact heartstone brings 1,800 gp.
This would be fairly reasonable to use in 5e as well. Naturally, the specifics are down to you as DM. For example, since the saving throws buff is not an official function of the 5e heartstone (according to the MM), you might want to remove that ability from it and adjust the sale price accordingly.
Nope, just the Innate Spellcasting ability (if that particular type of hag has that) which does not use slots. The spell slots are a special feature of the coven, and that feature specifically says it only works when all members of the coven are within 30 feet of each other.
I don't see anything about a spellbook — the hags do, however, have a limited list of spells, and it is perhaps an artifact of Roll20 that this list is presented as a spellbook.
The spells are described as being from the wizard spell list, and unlike the innate spellcasting, they're intelligence-based. If you, as a DM, decide to add wizard class levels to a hag following the guidance in the DMG, it would seem reasonable to put these spells in a spellbook. And even without that, a book with these spells seems like reasonable loot when defeating a coven, if you've got a spell-collecting wizard in the party.
Best Answer
A dead hag cannot be a member of a coven
Once a hag is killed it is no longer considered a creature, and becomes an object. That is supported in this answer, and these (non-offical, but still fairly authoritative to some) tweets.
A dead hag stops being simply a hag (for rules at least), and becomes an object (likely called a dead hag, or hag corpse) which cannot be part of a coven.
This also makes sense narratively, the remaining hags would have to reform the coven by finding a third hag, so that
As suggested by @erik this could be a great reason to allow hags to make death saves.
Just make this clear to the players in the way you describe them being reduced to zero hp, because it is unusual so they might not fully understand these hags work differently to most creatures.