I met a girl online and I want to visit her in Shanghai

Do I need to book the hotel before applying for the visa?
Do I need an invitation letter from her?
Can I buy the plane ticket before getting it?

I'm actually in japan, and I have spanish nationality. It seems that you can apply here at travel agencies, but I don't have a letter from her. It would take a while, but I want to buy the ticket now while it's cheap.
Thank you very much in advance.