Review:
Lore: None, Dx. Seeing a champion without lore makes me sad.
Stats:
There aren't any numbers but I don't see any real problems with the approximate values except maybe that he's a little bit more durable than many AP casters.
Abilities:
Passive: So this is kinda like a combination of Orianna's and Jax's? I know you are considering something else and I encourage that. The combination of these two abilities basically means that he can build pure AP and be half of an AD carry as well. Jax's passive is powerful but limited by him being a melee character. Putting this ability on a ranged character is too much, IMO. Admittedly, Jax gains much larger bonuses to Attack Speed but it is also his only passive.
Q: Now, I know you were looking at Miss Fortune's ult when you made this ability for balance. Half the range and half the damage (due to dealing damage every .5 seconds instead of .25) might make up for a debuff, improved scaling and a cooldown 1/10 as long. I don't know. It's up to you to decide.
W: I'm not quite sure what this ability does but whatever it is it doesn't seem too powerful.
E: Frankly, I like it. The only problem I have is that he needs to use another ability to activate the secondary effects. With the cooldowns on his abilities that might represent a problem.
R: I like it. It's cool and innovative. It does deal a lot of damage so you may want to look at the cooldown but other than that I have no complaints.
In addition, I'd say this champion could benefit from changing cooldowns (start high but lessen as the abilities level up) on all his abilities.
I guess my big suggestion is with the Passive and the E. What do you think about changing his passive to "Whenever Tychus attacks or uses an ability, he gains 5 / 6 / 7 / 8 / 9 / 10 % (improving every 3 levels i.e: 1,4,7,10,13,16) magic penetration for 3 seconds, stacking up to 4 times." Alternately, it could shred MR on a single target hit by his auto attacks. Then, I'd change his E to be "Tychus blinks to the targeted location, causing his next autoattack or ability to deal (6 / 8 / 10 / 12 / 14%) extra damage and silence the enemy for .75 / 1 / 1.25 / 1.5 / 2 seconds."
Anyways, it's a cool idea for a champion and I hope you flesh out more than his abilities soon.
If you have time, maybe you could review Oberon, Protector of the Glade