What are the visa requirements to visit China for travel purpose?

Usually, a single entry tourism visa allows 30 days' stay in China. I think 30 days are enough for your traveling in China. I don't know how many cities are you going to visit so i cannot tell how many days should you stay. FYI: a golden triangle tour in Beijing, Xian and Shanghai usually takes half a month.

You cannot apply for the visas with only one passport. Requirements for applying for China tourist visa:
1. applicant's valid passport (at least six months before expiration) with blank visa pages and copy of the first three pages;
2. Typed Visa Application Form (Form V2011A) with one applicant's passport photo.
3. For tourism, Invitation letters in Chinese language by individual/entity in China and six-month bank statement is required
4. Applicants who have never been to China before should submit in person.