How long does it take from Zhengzhou to Beijing and Shanghai by train? How often is each service?

The only one bullet train between Xian and ZZ will take about five hours and forty minutes operating between the two cities. Other fast trains will take about six hours and a half.
To Shanghai, the bullet ones will take you about seven hours and others will take you eight to ten hours.
As for operating time, you can refer to https://www.travelchinaguide.com/china-trains/ to find more.