My flight is going Zhengzhou.. i would like to visit Luoyang (Shaolin) and KaiFeng during my visit.

Hello, Angeline, the transportation is quite convenient. Upon landing at Xinzheng International Airport, there are several direct coaches that can take you to Luoyang and Kaifeng. Hereunder is the detailed information:
To Luoyang Jianxi District Peony Square, the buses depart at 10:00, 11:00, 12:00, 13:00, 14:00, 15:00, 16:00, 17:00, 18:00, 19:00, 20:00, 21:00, 22:30 and 23:30. The ticket fare is CNY 70 per person. After arriving, take a taxi to Luoyang Bus Station. There are frequent buses to Shaolin Temple.

To Kaifeng West District Haode Roundabout: The bus schedules are 09:30, 10:30, 11:30, 12:30, 13:30, 14:30, 15:30, 16:30, 17:30, 18:30, 19:30, 20:45, 22:00 and 23:30. It costs CNY 40 per person.

Thanks.. would like to check whether there are any buses at luoyang bus station to Kaifeng? Other than buses.. are there any transport going back to ZZ City? And how long does the journey takes from airport to Luoyang?

Yes, there are buses operating between Luoyang and Kaifeng. The operating time is 08:25 to 15:00 with the interval of 0.5-1.5 hours. The ticket fare is CNY60/person.
You can take train at the Luoyang Railway Station or the high speed train at the Luoyang Longmen Station to ZZ. There are lots of trains operating in one day.
From ZZ airport to Luoyang, you can take the airport shuttle bus which will cost CNY70/person. It operates during 10:00 to 23:30 with the frequency of 1 hour. The duration may be around 2.5 hours.