I like the concept, but there's a few things I'd change. But one of them is more noticeable than the others.
Q:Infected path-
Gevaar sprays the ground for 3 seconds, creating a path that deals 20/30/40/50/60 + 4/5/6/7/8/9%(+1% for every 50 ap) of the targets' health in magic damage every second. (You are able to move cursor to create the path)The path lasts for 3 seconds after Gevaar is finished making it, and also slows enemies by 25/30/35/40/45%. He cannot move or use any other spells during this time. Activate again to cancel.
That's a metric fuckton of damage right there. +1% for every 50AP + up to 9% in targets health? Per second? That's like a bazillion damage. I like the attacks concept but that's wayyyyyyy overpowered.
His passive seems pretty good, but health regeneration doesn't really do much while you're actually fighting. (Unless it's some huge burst amount). I would instead make it more useful, require more skill, but also be a lot more interesting. Enemy champions who get within 425 units of Gevaar get a debuff that deals more damage to them over 7 seconds depending on how long they were within that range. Example: Tryndamere is within your range for 6 seconds. He takes no damage until he leaves that range but once he's no longer near you the debuff activates and does something like 300 Magic Damage over the next 7 seconds. Likewise if Ashe is near you for only 3 seconds she will take 150 magic damage over 7 seconds once she leaves the area. If you die before they can leave your area they still take the damage over time. This is because radiation deteriorates your health, not just your ability to heal. I feel like this change would make the passive more useful and strategic than what you previously suggested. (Caps at 500 damage BTW to prevent it being OP) This would make enemy champions think twice before engaging you. It could be toggled on and off for ganking and hiding in bushes. Will not proc Liandry.
You should then change his W to a jump/escape mechanism so you can capitalize on your passive damage.
E and R seem massively overpowered as well. Maybe reduce the damage of E and make it 650 range limited to 5 minions and 2 champions. Gives him wave clearing potential.
I don't even know where to start on R. 90% AP every second for 6 seconds? 540% AP damage? I would replace it with a skill passive that grants him 3/5/7% of the damage inflicted by Radiation back as health for sustain. And he can activate it to increase his passive Radiation's range and damage by 150% (up to 1250 damage to everyone in 1065 range over 7 seconds (after the ability ends/they leave range), and he gets healed by 7% of all that too.