If a split card is both an instant card and a sorcery card, it's only counted once for The Magic Mirror's cost reduction ability.

Once you announce that you're casting a spell, no player may take actions until the spell has been paid for. Notably, opponents can't try to change by how much a relic's cost is reduced.

The cost reduction ability reduces only the generic mana in the relic's cost. The colored mana must still be paid.

If The Magic Mirror leaves the battlefield while its last ability is on the stack, the ability will use the number of knowledge counters The Magic Mirror had before leaving the battlefield to determine how many cards you'll draw.

Adventurer cards aren't instant or sorcery cards while they're in your graveyard.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.