Are the problems with nostrification likely to occur if higher education institution does not exist any more?
Upon expertise the enquiry if higher education institution has valid license for educational activities and state accreditation at the moment of issuance a diploma to your is made. In your case the enquiry may me sent to the national education administration body.
Do I need nostrification if I do not want to get the second higher education in Russian higher education institution, but just want to improve my professional skills within the level of education I have got already? (Advanced courses)
Education institutions develop the conditions of entry to the advanced courses themselves. As a rule, the citizenship of a student is not important, and diploma nostrification is not required. It is better to learn the entry conditions in education institution where you are going to get advanced courses.