Hot and cold press does count for paper, too. Illustration board is nothing but paper (usually bristol) backed with cardboard. Hot press is smooth, in illustration boards it is VERY smooth like glass, and the colors tend to lay on the surface. Cold press has "tooth" (in variable amounts depending on the brand) meaning it has a texture, and the colors tend to soak in.
Actual rag watercolor paper has both hot and cold press, but even the hot press will have a little texture because it is made for watercolor. Hot press illustration board is not usually used for painting (although I know artists who do), but is primo for inking. In my gallery you'll see my color work is all done on cold press, but the inked "Follow the Leader" is done on hot press. That extreme crispness of line is due to hot press not allowing the ink to bleed at all.
I can't help you with watercolor pencils, since I've only ever used tubed watercolor, but I will say that it is a common thing for artists who are just starting out learning to use tiny brushes. At the university, the art teachers were always trying to get students to use bigger brushes. A good brush will have a precise point no matter what the size of the "belly," but the "belly" is where all the paint is held. Too small a brush and you have to recharge it too often, leading to choppy strokes instead of smooth.
I don't use anything smaller than a 4 and mostly a 6, even though I rarely work larger than 12 by 15 inches. But I will admit that I am totally spoiled by using only pure sable brushes. Expensive, yes, but SOOOO worth it. Precise points even in the huge sizes and they hold more paint for their size than synthetics. But don't EVER "scrub" with them! You don't want to wear off the points!