Almost all of the things I wanted to say have already been said so this one is probably going to be quite similar to the rest.
I'll try to incorporate the requirements you set out.
Name: Valanth the Crusader of the Cosmos.
Passive - Cosmic Cleave: 10 second static cooldown. Every few seconds, Valanth imbues his sword with cosmic energy, causing his next basic attack to deal 5 / 10 / 15 / 20 / 25 (+ 100% AD) (+ 50% AP) bonus magic damage in a cone in front of him. Basic attacks reduce the cooldown of Cosmic Cleave by 1 second.
Q - Singularity Spike: Valanth shoots a singularity spike at the target enemy, latching unto it. After a 2 second delay, it explodes, dealing 25 / 50 / 75 / 100 / 125 (+ 50% AP) magic damage and slowing all enemies in a 500 radius for 10 / 20 / 30 / 40 / 50% (5% per 100 AP) for 2 seconds. Every enemy slowed reduces the cooldown of Cosmic Cleave by 1 second.
Counterplay against mobile champions and ranged poke.
W - Gravity Shift: Valanth harnesses the power of a moon, causing gravity around him to become stronger in a 500 radius for 1 / 1.5 / 2 / 2.5 / 3 seconds. Enemies inside the area are slowed by 10 / 20 / 30 / 40 / 50% (+5% per 100 AP) and are Grounded. Any dashes and or projectiles that enters his Gravity Zone are negated and the enemy is immediately Knocked Down. Negating a dash or projectile reduces the cooldown of Cosmic Cleave by 1 second.
Fulfills the requirement of both being a counterpick against mobile champions, being good against enemies with projectiles, and it doesn't deal any damage.
E - Dimensional Shift: Valanth temporarily phases out of this dimension gaining 10 / 20 / 30 / 40 / 50% (+5% per 100 AP) bonus movement speed and becoming stealthed and invulnerable for the next 0.5 / 1 / 1.5 / 2 / 2.5 seconds. Being hit by a spell or abiltiy reduces the cooldown of Cosmic Cleave by 1 second. Valanth can still cast abilities whilst shifted, but can't basic attack, use summoner spells nor use item actives.
Bonus movement speed helps provide counterplay against mobile champions and untargetability provides counterplay against projectiles.
R - Time Warp: By harnessing the gravitational forces of the universe, Valanth warps the flow of time, accelerating all allies, including himself, allied champions, minions, structures and pets by 10 / 20 / 30% (+1% per 100 AP), whilst deaccelerating all enemies by 5 / 10 / 15% (+1% per 100 AP) for 10 seconds. Things Time Warp accelerates/deaccelerates include:
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Health regeneration.
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Resource regeneration.
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Attack speed.
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Movement speed.
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Cooldowns (both passive, ability, summoner spell, rune and item cooldowns)
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Cast time.
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Channel time.
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Projectile speed.
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Dash speed.
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Debuff durations (including crowd control effects).
Fulfills the requirement of a global effect and is still counterplay against mobility and projectiles and it doesn't deal any damage.
I hope this wasn't a waste of everyone's time.