Firstly, Moses was not a good public speaker and was reluctant to do God's bidding. Second, It was not suddenly he went away and came back with 10 rules; God directed them to do this.
Exodus 19:
1)In the third month, when the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai.
That is hardly a long time. 3 months is only 90 days. They were in forced slave labor for over 200 years. 90 days is nothing after what God did to get them out of Egypt. The people were restless from staying leaderless in one spot too long and reverted back to idol worship they picked up from the Egyptians. That is the anarchy you are referring to I am assuming.
To your edited: God chose to not base the belief in him on miracles. Sure God can perform them at will, but if people only believe in God because they got something at first, they will want something the next time they need a miracle as well. God is not a dog that he would perform tricks. Faith is something that is required, for "without faith it is impossible to please God." If you require miracles for you to follow God, you are not using faith.
