We can gate in the beach scene without it seeming artificial by having there be a pile of debris or something that you have to destroy to get through. Once the player is through we can be sure he's chosen a class, and that he knows how to perform a melee attack.
We don't have any places in the main game that you'd need to blink-jump to get to, but it comes in handy for dodging enemies. I think the blink ability would be better served if we made there be some big creature that you had to get by. He'd start off asleep, and he'd be powerful enough that if you attacked him you'd die. The only way past would be to blink past him.
Similarly, while I like the idea of burning down a spiderweb, it wouldn't translate to the rest of the game, especially if we used spiderwebs as decals at all. I think it's probably best for the ranged attack segment of the tutorial to be the same for all the classes.
For the lightning: Maybe there could be a guard or something holding a gate closed, but he's on the other side of a wall, so you can't target him with a fireball.
For the shield we can put the player against a whole bunch of archers ( making use of the damage variances to give them little to no melee damage).
Ranged: Need to hit a lever that's out of reach. Opens a door.
Caltrop: Maybe we could make caltrops slow the enemies down and only do a tiny bit of damage. Then maybe we could put the player in a situation where he needs to run away from an enemy that's much faster than the player.
Idea for the shield tutorial: We could have each arrow that hits the player cause 1 or 2 damage to the archer who shot it. So we could have tons of archers, and as the player defends, the enemies will eventually all run away.
Sounds good. And how about the lever you have to hit will be the one that opens the big tower door? And so while the door is slowly opening, the player is trying to dodge arrows, like you mentioned in email.
Idea for the caltrop tutorial: What about having there be a point where you have to drop off a platform, but there's an extremely powerful enemy blocking your way? Essentially it would be impossible to progress without using it, or you'd die every time. I think it would be more intuitive and immediately obvious as to what's going on.