You can activate “Meteorain” during your turn at any point from the Draw Phase to the end of your Battle Phase; you cannot activate it during the Damage Step, Main Phase 2, your End Phase, or your opponent’s turn.
“Meteorain”’s effect applies to all your monsters. Monsters that you Summon, Flip Summon, Special Summon, etc. after activating “Meteorain” still get its effect.
When you attack with a monster that has “Meteorain”’s bonus, and you attack a Defense Position “Amazoness Swordswoman”, then you will take the Battle Damage to your Life Points.