Just start my PhD study recently and there is a job offer coming. Because I self-fund at the moment, is it possible for international full-time student to change to part-time PhD? How long is the Part-time research, 9 years? Is the tuition fee half of that Full-time one? Who knows? Please give some suggestions.

I would have thought you would have to ask your university.

Ask your university and let us know what they say. A part-time PhD could take 5-6 years. Part-time fees should be half. Your right to work in the UK as an international student would usually only allow you to do paid work for 20 hours per week and would not allow you to pursue a career by taking a permanent full-time vacancy. You can apply to the home office for permission to accept the post if it is more than 20 hours per week or a permanent position.