If you want the scholarship for your degree, this does not mean that you will definately get funding for preparatory study. If you do then you may not get it for your degree. Check with the scholarship boards you are approaching.
You will probably be expected to be at HSK4 before you commence your degree course, an additional year.
In this case you can study for HSK anywhere (self funded), and then do the degree somewhere else.
When I looked at study in 2006.
It seemed that the top courses were in the International universities in Tier 1 cities.
If you want HSK you may need to go here.
The best programme for Chinese study used to be at Shanghai Jiaotong University. At the time they were the only univesity that taught western students in different classes, as we have a different learning/teaching method.
Some classes are full of Japanese and other Asian students who are used to rote learning. Japanese students can also read Chinese charachters, and you can fall behind in reading and writing very quickly.
Shanghai Fudan had a policy of rooming Chinese and foreign students together. This is great for cross cultural learning. Perhaps something to ask for.
Beijing WenHuaDaXue had lost its lustre. The courses are out of date, and the University appears to have been resting on its laurels for too long.
There are arguements for and against 'Normal' unis.
Against - you can get some trainee teachers.
For - the focus is on teaching. Learner teachers are supervised. Teaching is more closely monitored. The institution can pick from their best students when the finaly recruit grads.
Some Normal unis (eg Shanghai East China Normal) have developed their own materials that are up to date and relevant.
By contrast, other unis can not guarantee quality of teaching, especially regarding resources.
Look for the unis with an international reputation. They have a better learning culture and are not fixated on profits, will have better resources, and teachers.
Almost every uni will offer a Mandarin course, but only a few can resource it properly.
Look for universities that offer HSK as a core subject. Some universities offer it as an option, this means if enough students sign up for it then they will engage a part time teacher. If not enought students sign up for it then no course. Unless it is a core subject area, DO NOT trust promises of admin people who will want to sign you up (no matter what).
I do not know what percentage of Kunming students will demand HSK
Yunda has lost its sparkle and is no longer the top uni in the province, let alone nationally, or internationally.
Final note.
Ask specific questions. The only stupid question is the one you did not ask.
e.g.
Q. Do you offer HSK? A. Yes.
Q. If I want HSK will I get it? A. Yes.
Q. How many students are studying HSK at the moment? A. I don't know (red flag probably being evasive).
Q. Can you find out for me? A. Yes (this does not mean anything).
Unless they come back with a definitive answer, you probably won't get HSK. Yes is not definitive.