I think the 1st level spell slot bonus is a bit op, I would consider lowering the damage dice to be more inline with the potential damage output of a first level spell (I Think 2d6 is good, worse then flame hands but that has a save attached to it). A better solution might be a bit of reordering. 2d10 damage on all targets from a third level spell is pretty balanced (similar argument to above, call lightning is 3d10 but has a save), and I think the bonus from using a 2nd and 3rd level spell slot were both kind of weak so pushing each of those down Should be balanced.
I'm not sure how to fix spell secret, changing the damage type is already a pretty strong ability, and I'd feel tempted to just drop the second part of that power. The side bar offers a potential solution, you could require your player to justify why their new save is the case. In the examples it makes sense what the new saves are based on their descriptions, but for example if be hard pressed to find a good description that would make something an Int save...
