They do.

I have HKS Coilovers on my S2K and have 2 finger space (fender to tire) at the front and rear. At mid damping setting, I hear no rubbing at all, but will rub at very soft setting and from big bumps. 3 fingers and still rub? I don't get it maybe firm up the damper setting?

Try rolling the fenders better, and or setting the pre load/bump and ride height properly to cap off the bump/compression before it hits anything. Adjusting damping to prevent rubbing isn't the best solution, it compromises the ride.

A thought, were bump stops properly installed with the coilovers?

They act as a supplemental spring. Without them, your spring rate, especially at larger suspension travel, is way lower than it should be (not to mention if you hit a big bump soke really bad stuff is gonna happen).

On a coilover with pre load and ride height separate adjustment, you are ideally supposed to set the shock body length to allow the bump stop to come in contact first before the tire hits the inner/top of the fender, then use the pre load adjustment to effect right height/bump travel amount and depending on your spring rate and your shock body length will determine where your resting ride height is more or less along with helper springs if needed to help this(usually do as stiffer main springs are used). There is always some amount of compromise if ride height is the primary motive, but never should the tire hit the fender or you aren't using the bump stops as intended, and will bend your fenders or burn up your tires/cause skidding.

OP has Ohlins DFV and 2mm is max preload on fronts,<not rear>adjust bottom fork for fender clearance only.<not spring preload>

I generally ignore manufacture set up guidelines on coilovers as one shoe doesn't always fit all depending on other modifications. But always good to fallow guidelines if you don't know what you are doing and why. I view them as a starting point, rather then an ending point. If you can isolate the spring pre load from the shock body length and utilize additional helper springs if needed, then you should be able to dial in everything the way you want without any pre load at all, which is ideal. Once I added stiffer springs to my coilovers, I added helper springs to be able to adjust ride height and bump travel to optimum levels again. The coilovers never came with helper springs from the factory.

Already on 6 clicks from full stiff (Ohlins DFV has 32 or 34 clicks total). A similar S2000 I read online has a similar wheel size and spring rate setup (also has Ohlins DFV coilovers) and does not rub with 8 clicks from full stiff judging based off his track videos.

Already rolled flat, but forgot to cut the metal tabs off (but the metal tabs are already rolled flat). Should I make an attempt to cut the metal tabs, even though they are rolled practically flat?

I think I should also check for my suspension bushings and for bent/worn out suspension components. Would that lead to a solution? I don't think the bushings has ever been replaced, and now I sometimes hear a clunking sound from the offending side whenever I turn (not all the time).

I don't think the suspension bushings has ever been replaced (2006 model year and the car is bought used, mileage is currently at 134,6XX miles).