Caroline. Always complete the Applications fully. Ensure you put the Hotel Address you will be at for at least the first night on it. Remember to also do this on the Arrivals Card they issue you with on the Airplane
You are in Thailand. You exit Thailand on your Thai Passport (by Air) and enter the US on your US Passport. You have duel nationality. So no issues. Why complicate the issue.....or am I missing something lol