Let me do a brief introduction to Individual Values.
Each type of pokemon has different base values for Attack, Defense and Stamina. However, each Pokemon is also randomly assigned a 0-15 bonus to each of them. These bonuses are called IV's (Individual Values). They represent genetic variance, in that some pokemon are just genetically superior to others.
Base stats are obtained from base Gen 6 stats:
BaseStamina = 2 * Hp
BaseAttack = 2 * ROUND(Atk0.5 SpA0.5 + Spe0.5)
BaseDefense = 2 * ROUND(Def0.5 SpD0.5 + Spe0.5)
Hp, Atk, Def, SpA, SpD, Spe are all the base values in Gen 6.
Then each value is obtained adding the base stat and the relative IV (with a common multiplier):
HP = (BaseStamina + IVStamina) * Multiplier
Attack = (BaseAttack + IVAttack) * Multiplier
Defense = (BaseDefense + IVDefense) * Multiplier
This means that IVs only grant you a bonus for each stats.
Regarding your questions:
Does a higher attack value makes Water Gun more powerful?
Definitely yes. Stats in Pokemon Go are like stats in the classic series, a higher Attack deals higher damage.
Does a higher attack value make Pokemon to response faster?
I don't think so, moveset has the biggest impact upon DPS (damage per second) and it has nothing to do with IVs.
Does a higher Defense value gives more HP or simply better defense?
As you can see from the formulas above, HP depends on
BaseStamina + IVStamina. So a higher Defense will give your Pokemon a better defense when attacked, like in the classic series.
Does a Stamina value gives more HP or it makes the Stamina bar to fill up quicker in gym battle?
Same answer as the previous question, HP is affected by
BaseStamina + IVStamina.
I can't tell you anything about the Stamina bar, at the moment.
More info on TheSilphRoad Reddit, source here and here.