Short answers, pulled from the story.
The Union State officially came into effect on the 26th of January 2000 after ratification by the National Assembly of Belarus. The legal foundation began earlier with an Agreement on a Customs Union signed on the 6th of January 1995.
Mikhail Mishustin currently serves as president of the Council of Ministers. The Council includes member states Prime Ministers, Foreign Affairs ministers, Economy ministers, Finance ministers, and the State Secretary.
Alexander Lukashenko promised to introduce a common currency on the 1st of January 2004 but failed to deliver that year. Plans pushed back to the 1st of January 2005 also failed before delays continued through 2006.
Russia and Belarus implemented joint military officer training programs creating what they called the Regional Forces Group of Belarus and Russia on the 10th of February 2009. These operations aimed at strategic and battle training taking place in February and March 2009.
Abkhazia and South Ossetia expressed desire to join though neither is recognized by Belarus. Moldova's president Vladimir Voronin announced plans to join in 2001 before shifting interest toward European Union integration.