So, as the title asks, how does he work?

Looking at Swordplay, I should be doing 18% of the surrounding dpsers damage as click damage (I have Sal Merman in there, which is why it's 18% instead of 15%). With the legendary gear, i then have a further 400% click damage bonus (5x)

Let's then hypothetically say my DPser deals 100 damage. I place Bush Whacker next to him. 18% of 100 damage is 18. Multiply that by 5x and you get 90 damage.

Now... why does my Bush Whacker then deal ~1116 damage per click? That is about 12,4x times more than what I should be doing. And sometimes this multiplier is a bit higher or a bit lower. Can some explain where these random megboosts come from?

Well, I know about the differences between HIS vs YOUR click damage, and how his base abilities work there (Thanks for trying to explain it though).

But HOW how could I forget the trinkets?! xD

I see now that my Trinkets boost my clicks damage by 1,140%... which is exactly the boost I was getting (which is why I used that numerical example btw). Wow, I feel really stupid now for forgetting the trinkets. Thanks for pointing that out!

Just a tiny correction though; The formula would be:
(100 * 30 + 1,000,000 + 25,000) * 11 = 11,308,000

The reason it's 30 instead of 5,5 is because all abilities like this are multiplicative (2 * 2 * 2,5 * 3 = 30) rather than additive (1+1+1,5+2 = 5,5 ... which then should've been 6,5 anyway, since he has his base 1 to add too).
Unless his skills are an exception and are additive, that is?

Anywho, thanks! Now I also appreciate the clickdamage trinkets quite a bit more :)

I hadn't really paid attention to it before so the thing that got me to first notice the impact of click trinkets on converted DPS was when I was looking at comparing Karen and Graham after he was released. She copies 1% of her DPS as click damage. He copies 10% of his DPS as click damage (although he's a weaker DPSer so he ends up contributing less click damage than her). But for each of them I was noticing that the actual click damage I was ending up with was different from that fraction of their DPS. Eventually I noticed that the discrepancy matched up with the bonus on my click trinkets.

And yeah, Swordplay is the same thing but for a fraction of adjacent crusaders' DPS. In all of these cases, the converted DPS basically gets to double dip into the trinket bonuses. DPS trinkets apply before the fraction of the DPS gets copied as click damage, and then click trinkets apply to that amount. I haven't been able to follow what's going on with RoboRabbit's capacitor (tooltip mentions a maximum amount that can be stored but it never actually seems to reach any limit) but I assume that it's something similar there as well.

Hmmmm.... Random thought... People dislike Warwick because his clicks are weak. His design is built more around making area-clicked targets take more damage from other sources (team DPS at least, not sure about projectiles, but I've heard that it does NOT boost damage of your next clicks) rather than having the clicks themselves doing that much damage. But what if the ability was tweaked so that the bonus DPS received as a result of his curse is allowed to benefit from click trinkets? (Example: Your team deals 1000 DPS. Curse of Weakness would currently be a 200% bonus, resulting in 3000 DPS. But maybe after the tweak a 100% bonus from click trinkets would change that extra 2000 to 4000, for a grand total of 5000 DPS. Or then again, maybe change it to be more like a poison effect, triggering half a second after the DPS tick to hit them with the bonus damage. So it's not a DPS boost anymore, it's a projectile / Deflect Evil type of attack with offset timing from the main DPS. And then it would be clear in the description that this attack is classified as click damage even though it's automated.) So his design concept wouldn't change much (the actual click damage would still be weak) but the bonus from him would gain a "double dipping" benefit similar to the other clickers.