If the spell that's copied is modal (that is, it says "Choose one —" or the like), the copies will have the same mode or modes. You can't choose different ones.

You can't choose to pay any additional costs for the copies. However, effects based on any additional costs that were paid for the original spell are copied as though those same costs were paid for the copies too. Notably, if the spell you copy was kicked, the copies will also be kicked.

You must pay all costs and follow all normal timing rules to play a card chosen for Jaya's second loyalty ability. For example, if you choose a land card, you may only play it during one of your main phases while the stack is empty, and only if you haven't yet played a land in the same turn.

Activating Jaya's third loyalty ability creates a delayed triggered ability that will trigger each time you declare attackers this turn (usually, this will only happen once). This ability will trigger even if Jaya is no longer on the battlefield. If anything needs information about the source of that damage, use Jaya's characteristics as she last existed on the battlefield.

The triggered ability of Jaya's emblem will copy any red instant or sorcery spell you cast, not just one with targets.

The copies will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. The new targets must be legal.

The copies are created on the stack, so they're not "cast." Abilities that trigger when a player casts a spell won't trigger.

Copies are created even if the spell that caused the ability to trigger has been countered by the time that ability resolves. The copies resolve before the original spell.