Your Questions, Answered
Can you brief about the trains in Uzbekistan
The fast train runs on route Tashkent-Samarkand-Bukhara and it carries passengers between the cities in 6,5 hours time. Additionally, there is an evening train on Fridays and Sundays.
A number of trains connect the capital city with more remote cities of the country such as Bukhara, Termez, Urgench and Nukus. There are intermediate stops in Samarkand, Karshi, Navoi and other cities. Carriages of all classes are equipped with beds.
New high-speed train connects Tashkent, the capital, and the Fergana Valley. En-route it stops in the towns of Kokand, Margilan and Andijan. The train goes through a 19-kilometer tunnel under the mountain pass Kamchik.
Can you find vegetarian food in Uzbekistan?
Generally difficult, but not impossible. If you eat salad and bread only. Most if not all local treats contain meat. I don't think there would be a day when you'll find a vegetarian restaurant in Uzbekistan. This is land of shashlik. It's better to procure food yourself from a supermarket while in Tashkent, and in other parts, you would have to cope with salad. Vegetarianism is not really understood in Uzbekistan, especially in the regions. Say "bez myasa" "g'ushtsiz" (without meat) when you order a salad, as occasionally the salad plate will contain sliced meat.
Train booking, Money Exchange, SIM Card
You can draw US dollars from cash machines, increasingly available in tourist places (e.g. smart hotels and restaurants), and convert them to som in banks and exchange offices. Neither banks nor cash machines are on every street corner so you need to plan ahead a bit or else spend time looking for these facilities when you need them. Best to make sure you always have some dollars on you to change, and plenty of som. Visa cash machines seemed to work, MasterCard machines were rare and I never got money out of one. So don't go to Uzbekistan hoping to rely on MasterCard!
Exchange offices also seem to accept euros and even sterling, though dollars are still the major hard currency. Card payments are increasingly accepted in hotels and restaurants but most places want cash. The som is technically convertible - banks display both buy and sell rates - though the only place you'd want to convert back is at the airport.
It's worth noting that there is an exchange office in the Departures hall at Tashkent Airport which will convert your som back to dollars as long as you can produce an exchange receipt. Failing that the duty free shop in the Departure lounge quotes prices in dollars but also accepts som.