What are the Russian regulations/form for a Russian child, aged 6 travelling abroad with mother (for several months): is father's written permission required?
According to Russian federal law, a child that goes abroad with one parent (guardian) does not require written consent from another parent, UNLESS another parent did not limit their child to leave Russia by submitting a written request to federal migration services (the way these requests are submitted has changed on 12/06/2019). When leaving the country with one of the parents the customs will check the list of children for whom such requests from other parent were made. https://www.atorus.ru/news/press-centre/new/46379.html
Hence, you need to be sure that no limitation exists for a given child by asking another parent or making request to Russian federal migration services.