1. I am happy to write letters but mainly for people I know enough so that my assessment of them is evidence-based. I try not to write purely subjective opinions about people in the reference letter. If you have worked with me or taken my class with good exam results, they can be easily the evidence in the letter. If there is or little evidence, it is hard for me to write the letter and it is hard for it to be convincing. The letter will not be useful to you.
2. If you think I can write a letter for you, please email me with your draft and the information of what you will apply for. You could also email me with other information about you such as CVs, transcripts, awards, etc. But please realise that it indicates that I do not know you well if you need to send me a large amount of information. My letter will not be useful if it simply summarises your CVs and transcripts, which all will be in your application anyway.

1. Yes. PhD scholarships are won through the competition among all the PhD offer holders. So it is difficult to predict how difficult it will be as it depends who applies.
2. In the past, the winners always had good GPAs from top universities in the world, and first-authored publications in the top venues in their fields. This is especially so for International students.
3. My impression seems to be that the PhD funding competition among the Home students is slightly easier, but I have no statistics to support this.

1. Yes. I have had experiences with good students who have publishable research.
2. These students are normally strongly motivated as they need to invest a lot of time and effort to research, in addition to their already overloaded academic and social activities.

1. My statistics based on my career indicates No.
2. Not winning a scholarship does not necessarily indicate a weaker background and certainly not a reliable indicator of the future performance during the PhD.
3. In the past, I have had self-funded PhDs publishing top-tier conference/journal papers.

1. Yes. I do accept self-funded PhDs. The answer is Yes and No regarding whether it makes it easier.
2. The key indicator I am looking for in PhD candidates is whether they will be able to do good research. Where the funding comes from is separate. Of course, not having to win the scholarship in the competition makes it easier for the candidate. But the bar for acceptance stays the same.