Does Jewish New Year’s day change every year like Chinese New Year?
The Hebrew calendar is based on 12 lunar months, with a "leap month" added every few years to make sure that the holidays, especially Passover, remain within their regular seasons. The Hebrew month always begins with a New Moon.
The Muslim calendar is based on 12 lunar months, which are shorter than the solar year, which is why Ramadan will creep around from winter to fall to summer to spring and back. A few years ago, Ramadan fell at Christmas time, now it is earlier than Rosh Hashanah. Next year, Muslims will be fasting in August (heh).
I am not familiar with the Chinese calendar.