You can't do anything in between drawing a card and discarding a card, including casting the card you drew.

Spells that target more than one creature and/or planeswalker you control cost only more to cast.

To determine the total cost of an opponent's spell that targets a creature or planeswalker you control, start with the mana cost or alternative cost that player is paying, add any cost increases (such as that of Kasmina's effect), then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.