I'm finishing my Master's degree in my home country in March of 2022. I've just finished my first year of Master. I have no publications or results yet, but my work is going according to plans and is very promising. Results will come. My current GPA is 3.78/4.00. My undergraduate GPA is 2.68/4.00.
I'm currently looking forward to some Ph.D. programs in some universities in Canada, the United States of America and Germany. I'm looking mostly for programs that have a recent publication impact in my field of research (Geometry Processing), which isn't a very strong field in my home country.
Unfortunately, my advisors do not have contact with any international researchers in my area for collaboration (they are new in this area too). They say it would be a better idea if I had some collaboration experience before my applications and aren't encouraging me to apply without previous experience.
But I want to apply for international Ph.D. programs. I'm already preparing myself for proficiency in English tests. I'm totally dependent on scholarships and grants to be able to finish any Ph.D. program. Submissions are probably going to start around September/October.
My question is: how should I write an admission letter without any prior experience with professors, researchers, etc. at the university I'm applying to? All I have by now is access to the publications of the professors I'd like to be my advisors. That's the origin of my interest. Should I approach these professors someway before my application? If so, how should I approach them?
Also: I'm an LGBT girl and will be a first-time immigrant. How to express my concerns about financial and psychological support during my Ph.D. while writing for the professors?
This is super new for me and I don't have much external support right now. I'd appreciate any help or advice.