How can I reward my students? There any reward system available within the site?
A colleague in the Educator's Network has set up a classroom monetary system, where students can use their lingots to buy pencils, etc. That won't help now, but maybe free homework passes or links to crazy cat videos in the target language or...?
Another colleague created a leaderboard around her classroom walls with cute little owls that the students wrote their names on. As they gain XP, they move their owls around the room. Maybe you could do something virtually?
There is not much in the Duolingo store at the moment, other than the things Lrtward mentioned. So we have to get more creative in the meantime.