As for Russia it is a great and to me a SAFE country to visit ( I can state that without prejudice since I have traveled to many countries), you just have to have common sense and you will be safe. The police ( OMON as they are called in Russia ) frequently patrol tourist areas, and have zero tolerance for muggings and harrassment of tourists of any kind ( which happens rarely anyway). As for your passport , it is not necessary to carry with you, leave it in the safe in the hotel room. Just carry a small amount of cash and the credit cards you will need. As for the subways... they are generally safe, only at night I would recommend to be with someone not due to robberies but sometimes drunken homeless people can annoy you, asking for money and they can harrass you ( just say go away/poshel proch and leave me alone and most will just leave). Also if God forbid if you loose your passport or have other issues, there is a Swiss consulate in Moscow. I hope you enjoy your trip. If you have anymore questions feel free to ask