The problem is that the game uses a font that doesn't support cyrilic symbols, so you need to change the font. Did you follow the 'official' translation method (generating translation scripts with Ren'Py SDK) or you are just replacing the text directly in the original scripts?
Either way, it's not that difficult, just take a look at the gui.rpy file and search this line
define gui.text_font
There you'll see the font used. If you are rewriting the original files in Russian, you just need to write there your desired font instead and then add that font (the ttf file) to the "game" folder
In the lines below that one you'll find other fonts used for other texts you see in game (UI menus, character's names...). You can change them the same way, if you're having the same issue there
In my signature there's a link to a translation guide for Ren'Py games. I'm rewriting it right now to add some better practices but the main points are still valid. Translator++ and other translation software tend to create bugs as translation engines have the bad habit of replacing some symbols like brackets and slash bars that are quite important in Ren'Py, that's probably the reason your first attempt was a failure
Edit - now I'm thinking it could actually be an UTF problem as
anne O'nymous says, since most of times when a font doesn't contain certain symbols Ren'Py just skip those, it (usually) doesn't add other symbols to replace them. So if the problem were the font used, it should be displaying absolutely nothing and not some strange symbols instead. But... well, check both solutions since sometimes Ren'Py has its own ways