trip planned to beijing,11-18/10/2013. passport valid until.30/03/2014.need to renew passport?

According to the rules, the applicants' passports must be valid at least six months when they apply for the visas. If you apply in September, your passport is valid for six months. However, I am not sure if the embassy will issue it to you since your passport is just valid for six months. If you have time, I think you'd better renew your passport in case of any unexpected situations.

Hi, I am traveling to HK and later China from 29th/09/2018 to 16th/10/2018. My passport is valid until 10th/04/2018, so now for more than 6 months, but would be less than 6 month once I leave CHina (16th/10/2018): Will this be a problem?

As long as you have valid passport and visa to enter China, I don't think it would be a problem for you to leave the country. Don't worry.