Can a friend who is currently working in china invite me?only family is mentioned on official site

Yes, the friend can invite you but you can only apply for L type with this invitation. It's not difficult for a single lady travelling alone abroad for the first time.

Except the invitation letter, you need to submit your passport, a photocopy of the passport, a properly filled application form attached with your recent photo, a personal statement and a work certificate or a bank statement of the latest six months.