Yes, you will not be qualified to apply for citizenship even though you come back to US every 6 months. To apply for citizenship, you need to live in US consecutively for at least 30 months in 5 years. Also, you need to file tax every year. So, if you really want to be a citizen, you might need to think about coming for good. In addition, you are taking a risk for each entry. Immigration can seize your green card any time (both entry or departure) if they believe that you are not really want to come to US.
If you need to go back to HK for work for a while, you can consider to land, wait for green card and apply for re-entry permit. With the re-entry permit, you should be given the allowance to re-enter US within a period of time but it is only temporary and will be expired. You can go to the website and check www.uscis.gov which is the government website of US Citizenship & Immigration Dept.
Chinese teacher has some kind of demand in cities with big Chinese communities but not sure how high.
花旗太太生活在花旗國,留意時差,你問我未必即時答到。