While I like the mechanics behind Brute, do we really need another generic fighter? Champion already does that pretty well.
I think in a few cases you could end up with 2 concentration spells, I'd probably allow the wizard to maintain concentration on both at once. A little power-up for a fairly niche ability.Brute is the 'Fixed' Champion, I'd say. People complain about how underpowered it is and this makes a correction.
School of Invention is odd - and perhaps too swingy. You give up control over which spell you cast. You have a 19% chance to try to cast 2 spells, which will fail 19% of the time. That equates to 81% chance of a 'random' (best of 2 options) spell, 15.39% chance of two 'random' spells, and 3.61% chance of no spell. Your random spell or double spells are not things you can choose, so you have to be prepared to have spells that are awkward to use in some situations (in a small room and you cast fireball?) However, it has some real power concentration appeal in converting 2nd level slots into additional damage to spike damage up. That might allow a wizard to get closer to being competitive with the melee classes on dealing damage to a single foe on a per turn basis.
The spore druid reaction mechanic is wacky. It should be a bonus action since it doesn't appear to be a reaction to anything and can only happen on your turn.
I would agree – either that or change it to “when an enemy moves within 10 feet of you” as the trigger.
Also, unless I misread it, the spore zombie cannot move, since it says it can only take the attack action. For lasting as long as it does, that seems a mistake – maybe it should be “can only take the move or attack action.”