If you can contact the receiving school before applying, you will be more likely to be approved. When you contact, you can tell the other tutor, come as soon as you get the national public school qualification, and so on. If you meet a kind tutor, you will be given an invitation letter. Anyway, there is no loss to TA. If you don't have an invitation letter, you can also apply for the national public school qualification, and then contact the tutor after the qualification is passed.
It is not the same application as the school and needs to be declared by the unit. When applying, be careful not to choose popular countries, such as the United States and Britain, if you are not sure.
If you apply for the qualification, the unit will keep your position and most units will pay you. The accommodation fee when going abroad is paid by the state, so just go to the education office of the consulate to get it. However, the funds sent by ordinary countries are not too much, just enough for your life. For example, going to Australia costs about 1200 Australian dollars per month.
When judging, the number of graduate schools and papers is important, but the most important thing is whether your research plan is true and feasible, whether it is needed by the country and so on.
Look carefully at the recommended websites, they will answer many of your questions.