If an agreement covering main issues related to upbringing of the child was signed by the parents such agreement is enough to obtain a Schengen visa and living abroad if provisions covering such issues are included in the agreement. As both parents are citizens of the Russian Federation such agreement shall be signed in the presence of a notary after consulting a lawyer and preparation of a draft agreement. The agreement may be executed in two languages. If citizens of the Russian Federation stay or reside abroad such agreement may be signed in a Consulate or an Embassy of the Russian Federation. I have a vast experience of drafting such agreements. Such agreements are signed by parents all around the world, they simplify relationships between ex-spouses and serve the best interests of minor children. Upon signing in the presence of a notary the agreement shall be apostilled in accordance with the Hague Convention dated 05.10.1961 signed, among others, by Russia and Belgium.
Termination of parental rights is not likely if the parents do not sign such agreement. Termination of parental rights is a measure of last resort applicable to a parent who evades discharge of his/her parental obligations or abuses parental rights. Father’s parental rights will not be terminated if the parents manage to come to an agreement about major issues related to upbringing of the child.
No maximum period between submission of an application for marriage registration and the registration is set by the laws but Vital Records Offices usually do not accept applications for marriage registration earlier than 3 months prior to the proposed registration date.
You should obtain a proof of your marital status in your Consulate in Moscow.