Is it safe to go visit Russia?

No country is totally crime-free; Russia is no different. Major cities such as Moscow and St. Petersburg see their fair share of petty crime such as pickpocketing, theft, etc. As in any big city, you should be careful of your belongings when traveling, especially when in crowded places or touristy areas.

Can a single Russian woman get a tourist visa to the US?

That single Russian women are almost never granted Visitors Visas to the US (or Canada/Australia for that matter).