(As we are only able to answer one question at a time, I have narrowed your question to one. Please feel free to resubmit your second question.)
Panem is clearly corrupt because of the drastic differences in the treatment of its citizens. We can see how the citizens of the capital are protected and isolated. They are well feed and have plenty of anything they might desire. Many of these people do not seem to work, or they work jobs of their choosing. The people of the outlying districts have next to nothing. They do not have enough to eat and people are literally starving to death. They are forced to work hard jobs with long hours whether they want to or not. For instance, the people of District 12 are forced into the dangerous and poisonous coal mines and the people of District 11 are forced to work in the fields to produce food. Of course, the produce and products produced in the districts is bound for the capital rather than the tables of the workers.
We see further corruption in the treatment of the favored districts closer to the capital. Those from districts producing valuable trinkets such as jewels are highly favored. The capital looks the other way while they illegally train tributes to win the games each year. These districts are provided with more food and support than the outer districts.
Panem may have formed out of necessity, but it has become woefully unbalanced. Those in the districts have nothing while those in the capital have everything. We can see the horrible ways in the which the capital desperately tries the hold the districts down.
Panem is corrupted because it is led and run by President Snow. He is the one who forces the traditional of the blood spilling of 23 tributes every year just to show who's really the boss. All the while he relaxes in the Capitol and terribly governs Panem while the other districts live a life of hard work and dealing with the sadness of possibly never seeing a loved one again.
2) Panam is corupt and run by the unpleasant Presidant Snow. He forces each of the 12 districts to have one girl and one boy participate in the Hunger Games. By him doing this, the act of rebellion takes place.