Due to sanctions there are no direct flights between Russia and the US, UK and the EU. However, you can easily come to Russia with a stopover in neutral countries. The most popular routes include flying via Istanbul (Turkey), Dubai (UAE), Belgrade (Serbia) and Yerevan (Armenia). Another option is to come to Russia by bus from Tbilisi (Georgia), Tallin (Estonia), Riga (Latvia) or Helsinki (Finland). Also, there are trains to Russia from Minsk (Belarus) and Almaty (Kazakhstan).
There are no signs of any intentions to close the border. Border closure makes no sense as those who wanted to leave have already done so. In any case, as a foreign citizen you can't be subject to mobilization and you will be able to leave Russia even in the highly unlikely event of the border closure.