Am on a student visa and not long ago finished registering a trade company here in China.

Nana, it's possible that you can apply for a L type from other countries like Vietnam or Thailand. However, I don't know why you apply for a business type. It requires a Chinese company to send you an invitation letter.

Yes, you can try to apply for a Z type because you opened a company here. However, the procedure is very complicated because you are the legal representative of your company. It's almost impossible for you to get it. You need to find an agency to help you do this.