Skill 1: I like this although it feels like it should be skill 3. 1st skill passives feel weird :P Poor casters
They just keep getting more heroes to screw them over.
Skill 2: I like this a lot. However, in 1 v 1 combat, a .25 second stun for every .5 seconds is a lot... I feel like it should be something like: "cannot hit the same unit more twice in a row unless there are no other valid targets. If a target is hit twice in a row, the 2nd hit will only deal damage." That just feels more natural. Also, it makes a .5 second stun over 1.5 seconds. So stunned 1/3 of the time. Otherwise, it's good.
Skill 3: TBH the armor reduction is out of place. Lightning reduces armor? :P Also, it doesn't synergize with your skill set. I see the effort to make him synergise with other heroes but really, the magic reduction is more than enough. I mean, a skill set is a SET. Lina contributes to the team via stunning but her skillset works by itself, for itself. Wisp is the exception but your hero seems more like a disruptor/AoE monster more than a support hero. Even Dazzle has an overall working to the skillset. So does Omni. The armor feels out of place. I think you can leave room for another effect.
Examples would be: "Drains mana equal to damage dealt and splits it amongst nearby allies. (maybe include the orb in mana giving)" or "slows at increasing percentages as they stay inside" or "magic reduction increases as they stay inside" or maybe even "converts all damage taken inside to magical damage (doesn't effect BKB'd units)" but don't reduce their armor. It's redundant and doesn't work with his skillset or even many of his ideal lineups in my opinion.
Skill 4: You have the hotkey set for Q which is the same as the 1st skill. I'm assuming you meant "R." Anyways, chain lightning is meh, damage is trash for an ultimate, especially since it can't bounce back to the same target, and the effects aren't very amazing other than the synergy of purge with your 3rd skill. Sounds harsh, I know, but I don't like the way it works out in your skillset. Sorry. I do have some fixes for it though.
Make him the bouncer, not the random projectile. He's invulnerable/magic immune(+take only 50% of damage?) during it and he bounces around, improving his ability to initiate.
Instead of attack silence, make it do something like "creates a magnetic effect on hit units, preventing them from separating more than X units from each other." So, when 5 heroes are hit, they can't move more than, say, 400 units from the nearest effected unit. I see lots of synergy with 3rd skill (requires a lot of coordination to escape) and with some other skills. Makes you less reliant on AoE disables too.
Also, the aghanim's upgrade should do a little more for cooldown. 15 seconds? Since the damage upgrade isn't all that great tbh.
OVERALL: It's a good hero, a few tweaks, tbh the 1st 2 skills really contribute the most to this but the hero is a good hero. I already pointed out what I didn't like but you did a good job
Feel free to check the signature for reviewing my Caspar suggestion