The first question: What he means is that he wants to somehow show a way that he can protest the hunger games before he dies. Show that he's against it, rather than acting exactly how the capital/ Snow wants them to act. Peeta wants to highlight each tributes individually/humanity
the second: there is 3/4 moments where Katniss understands what that means.
The hunger games
1. After Rue dies, she decides to cover Rue in flowers/mourn her. Ra
Catching fire
2. rather than showing off for the game makers do something that would piss them off
3. when in the arena acting against your self-interest is protesting the games
Mockingjay
4. that the careers/ people in 2 are just as much slaves as people in 12.