Summary:
Peter is in Antioch when others from the church in Jerusalem arrive. Peter falls into old habits of exclusion and works and acts/eats with the implication that the Gentile believers are “unclean.” Paul calls him on the carpet and gives a strong conviction that you either continue to try to live by the law and fail in so doing or you live as a free man saved by Jesus. You cannot and should not live as a slave while claiming to have been set free.
Questions:
12. Peters’ actions of not eating with Gentiles because of adherence to Jewish dietary restrictions did two things to cause Christians to stumble: (1) it encouraged a class system and/or separation within the church. We all understand the divisiveness that can come from not allowing all to drink from the same watering fountain – to not dine at the same table was equally divisive. (2) it held back the acknowledgment that Christ had provided full and complete justification by saying (through actions) that His gift was insufficient and additional actions and/or behaviors were required.
13. Peter acknowledged Paul’s rebuke in light of both the scriptures and direct revelation that had been bestowed upon him (Peter). However, he also acknowledged that Paul’s methods can be difficult.
Conclusion:
This reminds me of the Jews of Moses’ day. Having been set free from the bondage of Egypt, they almost immediately long for the comfortableness of a well-lived pattern, even though that was slavery. They even request to go back to be slaves in Egypt. Now, Christ has died, Christ has risen, the price of sin has been paid, the believers have been set free, but they pine for the pattern of slavery under the law.
The Notes are Good 
Wow this is brilliant, in Australia we are doing this lesson i have just finished mine and i was reading through what you wrote it is such a challenging study!
Blessings Han 🙂