Hi Malgo
https://www.lonelyplanet.com/mongoli...getting-around
I came in by train from Beijing to Ulan Bator. I applied for a Mongolian visa in Beijing which took a week so I went to Xian to see the terracotta warriors while I waited. I exited by train from Ulan Bator to Irkutsk. There were some pick pockets in Ulan Bator which was not safe at night but okay in the daytime. I applied for a Russian Visa in UB and it was ready to pick up when I got back from the Gobi. Good info here too:
https://www.seat61.com/trans-siberia...to-beijing.htm