I haven't tried the Neo schools, but I would like to see a greater level of differentiation between schools. I think your description of these Neo schools fulfills this need, and is something I'd like to try in-game.
Yes. I think each school should have some extra-powerful abilities that require additional effort than just gaining levels.
I've found a number of biped schools very difficult to get started in, especially for someone who is used to how dragon combat works. I'm all for a reimagining and rebalance of the schools.
I can see this working well for a few schools that rely on bursts of damage in combat, assuming that the spell and ability cooldowns are reduced to make it meaningful. Since druids rely on the power of nature, it makes sense that their power draws off of nature's mana, which replenishes over time.
This depends on how well you can keep the other schools distinct from druids, and how well you can develop these new mechanics to allow for greater synergies between multiple schools. If implementing mana means the magic schools have to be all bursty and play the same, then I'd say no. But if you can give each magic school a unique area of strength (which can be combined with other schools' unique strengths), then absolutely go for it. I can think of a few specializations for magic schools:
Mage: Flame spells cause area damage and burn damage over time.
Druid: Drawing mana from nature, fast mana regeneration and expensive spells (or just a smaller mana pool?) cause heavy, bursty damage to single enemies. Retaliation damage to attackers.
Spiritist: Steals health and mana from enemies.
Battle Mage: Melee hits replenish mana for spells and magic abilities, and spells give time for stamina to replenish for melee abilities.
Blood Mage: Uses own health instead of mana for spells.
Conjurer: Ice spells slow and freeze with area effect.
Shaman: Weakens enemies physically before poisoning them with blight damage over time.
Sorcerer: Weakens enemies mentally before frying their brains with mind damage.
Wizard: Energy spells cause chain damage that arcs between enemies and stuns them.
Multiclassing is one of Istaria's strong points, so take full advantage. Maybe the Spiritist school could be mainly about stealing away life and mana from enemies, which could help fuel the Druid school's spells? And if you run out of mana, you still have the Warrior's swords or the Monk's fists.
Yes, but I'd also like to know how it differs from the blood mage.