For the 74th Games (her first time in the Games), Katniss was not really sure she wanted to cold-heartedly kill other people her age. Because of this, she normally spent most of her time avoiding the other players.
Her avoidance of the other Tributes ("players" of the Games) helped her last through the entire Game. This also meant that the other Tributes would have to fight each other, leaving less killing for her to do. But because it's a book and there must be twists, Katniss and Peeta are the final two left in the Game, and therefore they struggle to both stay alive through the Gamemaker's various challenges sent to the two.
At the very end of the 74th Games, because Katniss and Peeta couldn't kill each other, Katniss and Peeta come up with the strategy to pretend to commit suicide with poisonous berries. The Gamemakers couldn't let this happen, so they spared their lives... But that lead to Muttations being released. Katniss developed a strategy to climb to the top of the Cornucopia and fight off the Mutts from there, as well as the last few Tributes at that time.
Overall, Katniss tried to lay low and let the main bloodbaths at the start finish. Then she'd still lay low and stay out of the fights.
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Yes, Katniss and Peeta both survive the third Quarter Quell, although Peeta is abducted by the capitol along with Johanna and Enobaria after the force field breaks, whereas Katniss (and Beetee and Finnick) are rescued by Plutarch Heavensbee.
Katniss and Peeta had the same strategy. Both of their strategies were to try to keep the other alive.
Katniss is telling the story in first person
The Hub is the name of the black market that Katniss trades at in The Hunger Games.
Katniss doesn't really have an offensive attack in the Hunger Games. She only kills one or two people (if you count Cato as her kill) in The Hunger Games. The only reason she killed them was to save others. So, her offensive attack strategy is to stay low until she really has to.
Katniss does (Katniss is Primrose's sister)
Katniss's stylist is named Cinna in The Hunger Games. Good book by the way.