Power up question.

The math is somewhat complex, but it's listed out here:
http://pokemongo.gamepress.gg/pokemon-stats-advanced

At the most basic level (and someone can correct me if I don't have this right), the tl;dr version is that a pokemon's CP is essentially a combination of base stats x level multiplier. So as you power up (i.e., level up) a pokemon, the level multiplier increases, which then increases the overall CP.

As CP is directly related to stats, another way of thinking about it is that every time a pokemon levels up, it's stats all increase by X (where X is a number determined from the level multiplier formula).

Attack and Defense increase at the same rate as Stamina, it's just that Stamina is the only value you directly see as HP

Yeah, the base stats won't change, but the IV's can increase it by 15 at last. For example, Dragonite has 263 attack base, with attack IV 15 = 278 attack. Which really changes on your Poké when you power up is the CP and HP (as you said).

Btw, the damage formula is this:
Damage = Floor(0.5 * (Attack / Defense) * (CpM_Atk / CpM_Def) * STAB * Type * Power) + 1

You can find more details in here: http://gaming.stackexchange.com/questions/275646/how-do-the-attack-and-defense-stats-work-in-pok%C3%A9mon-go

It's not a stupid question imho; I took quite a while to understand it, too. The details are explained in the section "Damage mechanics" of this page.

The damage an attack actually causes is roughly proportional to the CpMultiplier (CpM) of the attacker, and inverse proportional to the CpM of the defender. CpM is about 0.6 at level 20, but 0.73 at level 30. Thus in a fight between otherwise identical pokemons at levels 30 and 20, the higher level deals about 50% more damage (0.73/0.60 vs.0.60/0.73).

The values given for DPS in the pages of the individual pokemon and their moves are based on the assumption that this multiplier is one.