Your example isn’t good because there is a possibility that your students will learn less well in the new environment than they do with the current teaching method. ‘Nothing to lose’ can be used in a variety of circumstances, but one is when the current situation is very bad. This student has not learned any English at all in the last year. He has nothing to lose by trying something new. We’re behind in the match and not generating any scoring chances. We have nothing to lose by substituting strikers for defenders. (We will lose if we don’t make a change)

Yes you can say it like that, but it is not very natural and entirely clear what you mean. If your Chinese students are exposed to a bad English learning environment. Such as being taught English by London or New York Gangsters and criminals. Their English will become peppered with language that is not desirable to learn for a University, College, School, work, job, visa, resident application etc. They should be exposed to a good standard English teaching environment. It does not matter if it is American or any other English. once they have a foundation. it takes only days and less than a month to learn the new nuances if they decide to move to another country.

Yes, you can say that. "Nothing to lose" means there is no risk of any harm or loss coming from doing an action - usually something that other people are scared of, because they stand to potentially lose something from it. This reminds me of Laozi page 48: 為學日益. 為道日損. 損之又損. 以至於無為. 無為而無不為. 取天下常以無事. 及其有事, 不足以取天下.

Nothing to lose is a phrase used when there is no risk involved in undertaking a certain action or activity. The way you used it in the example you stated is correct. Another example is I have nothing to lose if I go on that trip.