1) Russia is generally very safe, and 2) I agree that the violence amongst children is crazy. It’s a great place to homeschool and free-range and I have not found a way to send children to school in a way that’s acceptable to us.
Russia doesn't have reliablr statistics on anything. It like saying North Korea is safe.
Larger cities have private schools. There are also embassy-affiliated schools (yes, even today).
In public schools there's this unofficial "letter grade system". Unlike the US, where kids homerooms are mixed around each year on purpose, in Russia a homeroom group sticks together through the entirety of their school career, grades 5-12. Of course some kids will move away, and new kids will join, but the core group remains. Many lifelong friendships are formed this way.
Now - and this part doesn't officially exist, but it certainly does in practice - these groups are not created equal. Let's say there are 3 teachers who are picking up a grade 5 homeroom. They will stick with these kids until they graduate. So, the teacher with the most seniority has their pick of the "best" graduating elementary students. These will be well-behaved and academically strong kids. Their new homeroom will be called 5A. Then the second most senior teacher has their pick. This homeroom will become 5B. And 5C onwards are the "leftovers". And these groups will stick together until they are 12A, B, and C.
If you want a good school experience for a nerdy shy kid - they have to be in "A". Of course, as a newbie who is unfamiliar with the system... your kid will likely be put in "C" ("ve"). And you probably know enough about how Russia works by now to understand how to go about changing that ;)