Visas required for the holder of an Irish passport traveling to Minsk via Moscow

One of my friends and I (holders of an Irish passport) bought, with a little too much eagerness, flights between Dublin and Minsk via Moscow.

We did not know that visa-free travel did not apply to travelers arriving from Russia.

I'm trying to understand what we should be doing to travel to Belarus, until now – it seems we need a A Belarusian visa, then two transit visas or a multiple entry Russian visa.

Is this hypothesis correct? We had planned to arrive in Moscow on a Friday morning and again on Monday morning, the transit visa only being valid for 3 days, we would need two?

My main questions are:

  • How can I apply for a Belarusian visa from Ireland?
  • Where can I get an invitation letter from a hotel?
  • Is it possible / preferable to obtain two transit visas for Russia or a multiple entry visa? Are you allowed to obtain a multiple entry visa for the sole purpose of transit
  • What would be the approximate cost of all required visas? It seems that the Belarusian visa is about 60 euros + 25 for the short-term stay – I do not know how much it costs a Russian transit visa.