if a move is labeled phys(physical), spec(special) does it mean it uses attack power, special attack power respectively?

yep .

Yep, it does. Not only does it depend on that, but if you're using a Physical move with a high Attack stat, and the other Pokemon has a high Defence Stat, your attack will do around normal damage. The same goes with Special Attack/Special Defence.

In gen 1, the special attack and special defence stat are the same, and is called "Special". In other words, Amnesia sharply raises both special attack and special defence. Have fun with Amnesia Mewtwo.

In gen 5, the moves Psyshock and Psystrike use the user's special attack, but go against the opponent's physical defence. So Psyshock will actually do less than average damage on a Cloyster, due to its extreme defence stat; on the other hand, Blissey who usually walls every special attacker, will take huge damage from Psyshock due to its low defence. I think there are other moves like Psyshock and Psystrike as well.

Before gen 4, moves are physical/special depending on their type. Normal, Fighting, Flying, Poison, Ground, Rock, Bug, Ghost and Steel moves are physical, whereas Fire, Grass, Water, Electric, Ice, Psychic, Dark and Dragon moves are special. This means that some Pokemon, like Gengar, have useless STABs (Gengar has a low attack stat, but both its types are physical). This also means that Skarmory and Blissey were even better back then, because Skarmory had no physical weaknesses and Blissey had no special weaknesses.

Hopefully that should give you all the info you need. Any other questions, you can check out stuff at http://www.psypokes.com