I really like the magic, it's the first one I ever went all the way with and I had a lot of fun watching my character's journey to becoming a Zar'akal.
I'm gunna go over all the 'schools' of Naz and give my quick two cents on them at the end of what I think is good and bad about them. Not going to go anymore in depth than that because I think it's the only part I can give meaningful critique on and I can't be asked to go over it all.
Malflame Manipulation:
One of the two starting schools of your default Naz. Conceptually, it's awesome. However, it has its problems.
Ups: Unlimited flavour. The ability to choose your own aesthetic and 1-emote manipulate it non-combatively is great.
Downs: Combatively, it's basically useless unless you're fighting an ST monster that isn't immune to it (this is not exactly common) or you're mogging on some dirt farmer without armour. There are notable exceptions with spells like Rok-dhuurz which for FOUR emotes can reliably make a single dent in someone's armour, or the Vhiit spell which you can use to jam your fingers into someone's helmet visor. In my experience, your first two combative spells (Vhiit and Rok-dhuurz) make up 90% of your malflame spell's usability in actual CRP that isn't between buddies, with the vast majority of other spells being under the category of 'nice to have', but they've never decided the outcome of a fight before in my experience.
What I think: I think giving some extra stuff to some of the other spells would be nice. The chain-whip spell for example could be used to hook around pieces of individual armour and yank them off, or you could make the pillar spell a physical object or heat up armour. Something to make me want to actually use the more expensive spells in more fights.
Demonology:
Again, another conceptually awesome school of Naz. This one however is actually as good as it sounds. You get to summon demons.
Ups: You get to summon things. This is always potent, regardless of the magic. The size of your court is well balanced, and honestly from purely the Naztherak's perspective there isn't much to say here but good things.
Downs: It might actually be a little too easy to make greater inferi, as others have said. I'm not sure, and honestly I don't think the easiness of making a demon really matters because the majority of people tend to fall off after a couple months of playing one anyway. That said, I wish we could use more of our npc summons in combat at once, as your standard imp is basically monster slop and the hellhound is only marginally better.
What I think: I think the problems with this mostly come down to the nature of the CAs that you're giving to people. I've never actually played a Zar'ei, but I've played an Akal. For most people, playing a pure evil character is actually quite taxing, but I've found ways to make my own fun out of it and overall I enjoy it. I don't think there are very many ways to fix this problem, as the people who will enjoy what playing a demon has to offer will probably love it, and those that don't will hate it. That's just the way she goes.
Cursing:
This one here is kind of a meme - for both good and bad, and it's the first of two schools that require you to permanently use a magic slot to take it. No one chooses this unless they're fully into the larp or because they're trying to go for full Zar'akal and they have to get it by requirement. It also needs to be broken up into two sections because it has two very distinct uses with their own problems.
[Cursed Idols]:
Ups: The larp potential is on full display here, and some of the curses are outright diabolical and funny to read. The idols themselves are not the problem and are honestly a fantastic component to the spirit of the magic, and I would argue is the only reason someone should take the school.
Downs: It basically requires you to only make them for people that you know will oocly play along, as any idol you give has a big fat [THIS ITEM IS CURSED] on the bottom of its description and if you try and trick people into taking it cold turkey, they will about 6 times out of 10 dump it into a chest or /use it after the roleplay has concluded. This is moreso the fault of the nature of LotC than it is the fault of the magic, however. But it IS a massive factor to consider when choosing to take this school.
What I think: I think that if you've stuck with a cursed idol for three OOC days, you should have some permanent narrative de-buff that sticks with you forever. A remanent of the curse, if you will. Nothing crippling, just something extra people can use to build a narrative around. Having to re-learn who you are after suffering the full brunt of Desolation or always being a little bit prone to illness after succombing to the curse of Pestilence would make this school have a genuine impact on the players that interact with Naztherak.
[Cursed Fire]:
Ups: There aren't any, really.
Downs: For one extra emote on any combative spell, you can put an aspect of your primary or secondary malice onto your malflame. The effects of these aren't very good, as they're not exactly impactful and they require a full extra emote ontop of a spell that could have already taken you like three emotes to summon in the first place.
What I think: This ability's just kind of shit. Either the effects need to be more impactful, or we need that blood magic marriage ammendment that let cursed fire be put on infernal fire rune imbued weapons. This is cool as a concept but in excecution there's literally no reason for anyone to use it. It needs something, because honestly if this got axed in a re-write as is I would not miss it at all.
Boons and Banes:
This is the second school that requires you to dedicate a spell slot, and it's much more worth it.
Ups: You get to be the devil and make deals with mortals in exchange for them experiencing a sliver of your power, but power always comes at a cost. This spell is one of the great examples of a spell that is powerful in presence, but kept balanced by well-rounded redlines and people's general willingness to create a story out of a bad encounter.
Downs: The spell itself I have no general problems with. The boons and banes are all pretty good. However, my one gripe is that if a person chooses they can literally just cut off the brand - and that's it! You can take a deal with a devil, and then just decide 'erm this isn't for me' and cut it off. There's literally ZERO lasting consequences for their in-character greed, ambition, or stupidity and they can just walk away and forget about it. I would prefer if they atleast make a secondary deal with the devil to have it removed or something.
What I think: I think that Boons and Banes is the stand-out of Naztherak in a good way. When you get it, it serves as a narrative symbol that you're well on your way to mastering the magic and have fully dedicated yourself to the cause as a full fledge Warlock, as you now have a permanent anchor to your infernal Lord. My only gripe is listed above, other than that I have only good things to say about it.