Dhaka-Singapore-Beijing-Mexico possible?

I have a Bangladeshi passport, with indian and mexican visa on it. We have 24 hours visa free transit at Changi Singapore. Is it possible to travel with transits at Singapore and Beijing and then take the Hainan flight from Beijing to Tijuana, Mexico? Is there any condition like the tickets must be under same pnr? or just any seperate onward ticket would suffice?

Aftab