Okay, big wall o' text coming, and all of what's below is based on my reading of the ability and some of the forums' discussion about it. Especially the "de-crit" thing! All of this is submitted humbly and without wanting you (the DM) to think that I'm trying to rules lawyer! Tell me how it works (or doesn't work) and I'll work with it in the way you said. Your job is hard enough (and I've DM'ed literally since the 70's, so believe me! I know!) without a rules lawyer in our midst!
This ability would probably be easier on a tabletop game, but only when the DM rolls their dice openly. That doesn't work here, of course. You (DM) will have to decide when "important spell" occurs. Just the normal damaging spells don't matter that much, but a save-or-effect or a finishing blow against a regenerating enemy would matter and be candidates.
Faerie fire on the two-headed troll would be a good example of something the bard would consider important, as that would grant Advantage on EVERYONE'S attack rolls against the four-eyed bastard!
On to the two Reaction abilities and their activating conditions:
Cutting Words - a priori, creature has to be able to hear Alisandra and (as far as she is aware) not be immune to charm (those are two prerequisites for the ability).
- Use case 1: someone's about to stab an ally who's already fairly hurt and the enemy rolls 9-13 on the d20.
- Use case 2: an enemy is going to try to resist an important spell and they roll 7-11 on the d20.
- Use case 3: this only applies if the -1d6 is actually reducing the number on the die (which is one way to read the ability; see below for a wordier explanation), so a 20 actually becomes a lower number from 19 to 14. If that's true, if a creature scores a critical hit on an ally, use Cutting Words to un-crit it. If you don't run it that way, delete use case 3.
Regarding Use Case 3: The relevant text from the ability "rolling a Bardic Inspiration die and subtracting the number rolled from the creature’s roll" does imply that it affects the roll, not the total result. I'm happy if you rule that it does affect the die roll, but I'm wanting to be 100% honest and open here: the majority of posters seem to think that it oddly-worded but it is still a negative modifier and that therefore it cannot undo a critical hit. A natural 20 always hits (and crits) and so even a -1,000,000 modifier wouldn't change that. The minority feel that it's worded that way deliberately and therefore isn't a modifier, per se, and alters the die roll itself. You'll have to decide and I'll be sure to use it the way you intend it to work.
Feather Fall
This case is much simpler -- if someone's falling and going to take damage/fall on spikes/etc., and they're in range (and this includes Alisandra herself or up to 5 total people), cast the spell. I suppose that if it's a small drop (like 10'), she would hold off unless people were already badly hurt. Or if the spikes were obviously dripping with bright glowing yellow poison or something...