Flying into Beijing for 5 days, then on to India. I know I need a regular visa to enter.

Flying home from India - via Chengdu and Beijing, 6 weeks after the Beijing stay. Not staying in either city. Not exiting the airport.

1. Will I need a transit visa?
2. Will I go through immigration in Chengdu, since the Chengdu-Beijing flight is a domestic flight.
or
3. Can I stay "in transit" the entire time in China (scheduled to be less than 24 hours)

Thanks for you help.