There are many levels of having an accent.
I know people who always speak with such a heavy accent that they are hard to understand. And I know people who have such a light accent that you need to know about the language they speak and be familiar with the local accent where they live to detect the accent at all.
Most are somewhere in the middle, speaking with some accent but not all the time and not always to the same level.
Something I have noticed that when getting tired, my accent and mistakes become stronger and happen more often. The same I have noticed in others who speak a foreign language much of the time. And one more thing, when people have spoken their first language, they tend to struggle a bit more with their second language, often just for a moment. (And that is not just a second language but also when talking with someone who speaks their home dialect or local accent, while usually they speak in an other dialect or other local accent.)
So you can have your Russian speak with a very light accent, only noticed when someone mentions it, and only when tired, stressed or after talking with others in Russian you adjust the language he speaks with the mistakes you mention in the question or those mentioned in the link in the other answer.
That is the way to avoid the irritating 'wrong' language in your text.
On the other hand, if you have them speak only rarely, it can be that you want a strong accent all the time, again by reducing the occasions they speak, you reduce the level of 'accent wrong language' mistakes in your text.
I find it annoying to read texts where I have to puzzle out every line written because it does not follow the normal language rules.
Best work it out to the level you are happy with. Your acceptance level may well be much higher than mine, and it is your book, not my acceptance you need to cater for.