Luoyang Railway to Shaolin to Longmen Grottoes to Luoyang Railway

Hi, I am coming from Xian to Luoyang in late Jun.
Train tickets
1) Should I book the train tickets in advance but sent to my country? Or easily avail if I buy on the spot?
2) Buying online thru your website seems require to pay CNY200 per ticket. So to and fro I must pay 2x CNY200?

Luoyang
1) From Railway to Shaolin, I should take a Bus to Shaolin. What is the bus number? How long is the travel?
2) From Shaolin to Longmen Grottoes, I should take direct bus to there? What is the bus number? How long is the travel?
3) From Longmen Grottoes back to Railway, I should take bus 81or 53? Duration 30 mins?

Cos I am travelling single, does the 1 day Luoyang tour USD239 accept for 1 person or min must be 2?
Thanks in advance.