Luoyang to Jiaozuo / Yun Tai Shan / Jiaozuo to Kaifeng

To be frank, one day is not enough to cover all parts at the scenic area. Usually, one and half a day to two days can be ideal. Besides, I remember the entrance ticket is valid for two days.

As for accommodation, don't worry~It is easy to check in on the spot. It is not necessary to book one in advance.

And as for the transport for your other two journeys, you are right that buses are more frequently scheduled compared to trains.
1. from Luoyang to Jiaozuo, buses are in ooperation from 06:30 to 18:20 every 30min. It costs CNY22.5 per person and the travel duration is around 2.5h.
2. from jiaozuo to kaifeng, the buses are schedule every an hour. Bus fare is aorund CNY37 and travel duration is 2.5-3h.

Thank you for your response. That's very helpful for my trip planning.

Do you know what time is for the last bus from Jiaozuo to Kaifeng?

I remember the last bus leaves at 16:00.

Another question is do I need to book these buses in advance?

No, you don't need to book the ticket in advance. Just go to the Bus Station to get the ticket and catch a bus.