I posted a discussion of purgatory in the "Spirits in Prison" thread a little further down. That'll be a little more efficient than doing it all over here.
As far as the candles are concerned, that's an old custom. It's an act of devotion. The offering box is to pay for the candles basically. I always put in a dollar, but the candles probably don't cost more than a nickle.
You can pray for anything. Note that you are asking the respective saint to pray for you, not to actually do any physical act. You can pray for deceased loved ones or for people who are with us now but may need our prayers. My wife asks the Blessed Mother to pray for our unborn baby.