What should be done if someone has eaten any form of Treif accidently? What should that person do? Also, what should a person do if he has eaten leavened bread on Pesach by accident? Does G-d give forgivness for a transgression like this?

Certainly forgiveness for an inadvertant sin is dependent on honest contrition and a commitment to be more careful in the future. That commitment should be strengthened by 1. learning more about the halacha one has broken. 2. thinking if there are ways to guarentee the trangression is not repeated. Some people give charity as a reminder that in the time of the temple a sacrifice would aid the repentance process.