There are some safety issues on trains to Central Asia but I think mostly these can be countered if you are sensible and don't leave your things about the compartment.
I haven't taken this particular train but suspect that there aren't too many foreigners who have traveled this route. It requires that you have a Russian, Kazakh and Uzbek visa and most people find that very expensive.
Train conditions should be like other long distance trains in Russia. I don't imagine there would be border crossing issues provided that your documents and visas are in order.
Class of ticket depends upon your budget. The prices can be seen using the rzd.ru website.
You might find it useful to read the New RU Train sticky for general information about train travel in Russia. Also see the Man in Seat 61 website for information.
Ruth