can I buy train tickets at Xian station for fast train to Luoyang for same or next day?

You can either buy the train ticket at Xian Railway Station or North Railway station. And you can certainly buy the ticket on the same day. If it is during the peak traveling days, you'd better book it in advance in case of selling out.
By the way, if you wanna book, the website may help you. I used it, and it works well.
https://www.travelchinaguide.com/china-trains/