Mir is pronounced like "mead" if you have the knack of making the D sound halfway like an R (slightly Indianish sound). Otherwise, just say "meer".
The word is not related to the Russian space station, though notably, as a Russian word it means or implies "peace", "community" and "world". That wasn't why it was chosen; it's just a fun coincidence from Mutt's point of view.
'Mir' is not to be confused with gender-neutral pronouns, because it's a title only.