Passive: Problem. With 500 AP, it will start off hitting at 100, but then your next hit will be 300. Plus your current attack damage, around 100. So basically 400 attack damage is kind of overpowered for a caster. Other than that, just a plain old damage boost.
Q: It's decent. Very reminiscent to Kayle's Righteous Fury, but it seems like it fits on this champion fine. Regarding the bonus damage, you should increase it - .3 of 500 AP is about 166, + 150 is only about 300. If you increased the damage though, it would be overpowered early game. You should give it a better AP ratio.
W: I like this ability. It is pretty much like Casseopea's, except for the fact that it will always stun one person and slow the rest. Now that I think about it, it is almost exactly like Casseopea's ult. I recommend changing it or adding something fun, or a new mechanic. Meh.
E: 42 is a lot of magic resist. A little too much in my opinion. Other than that, I like it. Again, it slightly resembled another one of Casseopea's spells, but you changed it a bunch. The damage (about 500 with 500 AP) is pretty balanced. It's like Annie's Disintegrate in terms of damage/CD. Nice spell, but I recommend toning down the magic resist.
R: Perfect ult, very fitting. Can be used as an escape, or placed right on the enemy team. The egg damage is perfect.
I like what you've done, but her damage seems a little crazy. Especially the passive. You should also increase the AP ratio of Q by a little so his Q does more scaled damage. The W isn't that creative, but the new targeting mechanic is. Nothing to say. The ult tops her off with an escape or a teamfight tide turner.
Creativity: Spider Queen isn't that creative, so I'd give you a 7/10.
Numbers: These are pretty balanced, but the passive is just to OP, and the Q is too not. 8/10
Skills: These are pretty cool, she has a main nuke, a CC, a movement speed buff and ranged attack. You did them in a cool way, so I will give you a 9/10.