Is it possible for skilled immigrants to New Zealand in this situation?

You two can immigrate to New Zealand with skills, which should be no problem. You have, and you have work experience in this field. In New Zealand's immigration policy, you are a long-term shortage of majors and a sustainable development industry. Preferably the principal applicant. Your education can give you 50 points, 10 points.

I don't know your age, but it should be about the same as your girlfriend, so your age is 25 points. But IELTS G requires 6.5 points.

The only problem is your relationship with your girlfriend. Can a stable cohabitation relationship be proved for more than one year? Note that marriage alone is not enough, it must be a marriage relationship of more than one year, or a stable cohabitation relationship that can be proved for more than one year. This requires your self-reported love history, proof from family and friends, and the same property in your name, such as car and house. Or a joint account of not less than 12 months. Otherwise, your girlfriend can't give you extra points. If these conditions are met, she can give you 10.

There is also the nature of your work unit. Only foreign-funded enterprises and joint ventures can give you extra points for your work experience. Otherwise, your work experience will not be recognized. If it is not a foreign joint venture, it should not be the main applicant. Let your girlfriend do it.

http://www.immigration.govt.nz/pointsindicator/

This is the New Zealand immigration calculator. take a look

The answer to the supplementary question. You'd better study English harder.

If your girlfriend is the main applicant, you only get 95 points. Although New Zealand's work experience can join without the automatic selection limit of 140, even a score of 100 is not enough to qualify for selection. In this way, she can only immigrate as the main applicant if she can find a relevant job in New Zealand.

If you can decide, the applicant will be very different. Things will be much simpler. Study English hard.