Can Americans fly to Mexico and then Cuba without agreeing any of the restrictions applied to?

No, Americans cannot fly to Mexico and then Cuba without agreeing to any of the restrictions applied. Travel to Cuba is heavily regulated by the United States government, and any American citizen intending to travel there must fall under one of the 12 authorized categories under the sanctions imposed by the US. Even when travelling under an authorized category, certain restrictions like mandatory spending of money on food, transportation and lodging within Cuba might still apply.