I am already an adult (≥ 18 years old) and have graduated from high school. What kinds of courses am I eligible to study in China after I have learnt some Mandarin?

Different universities set different requirements concerning the level of your Chinese Language, usually based on HSK 
results or college entrance exams. Actually, if your Chinese has reached a certain standard, you can apply for the following 
programs:

 
Non-degree Chinese language and culture courses

Almost any of the undergraduate degree courses in Chinese universities

 
Besides, for some Chinese-taught courses, you would attend classes with Chinese students, which can create
 an excellent environment for you.
 (The tuition rates for undergraduate Chinese-taught courses are usually 1500-4500
 USD a year.)