Hi!
I'm now having a hard time with “could produce” type of lands' abilities.
Let's say player controls Gruul Turf and Reflecting Pool and their opponent controls Damping Sphere. Will Reflecting Pool produce either {R} or {G} or Damping Sphere effect will apply here so he can only get {C}?

I suspect that {C} is a correct answer but would like anyone to confirm it.

Thanks in advance

Reflecting Pool will indeed produce only {C}.

The types of mana a land “could produce” include any type of mana that any ability of that permanent would produce if it resolved right now, and all applicable replacement effects are taken into account (in any possible order, if there's more than one) when figuring that out. Thanks to Damping Sphere, the only type of mana that Gruul Turf could produce at the moment is {C}, so that's all you can get out of Reflecting Pool.

This is explicitly laid out in Magic's Comprehensive Rules CR106.7, if you'd like to see it written out in full.