If you pay the evoke cost, you can have the creature's own triggered ability resolve before the evoke triggered ability. You can cast spells after that ability resolves but before you have to sacrifice the creature.

The owner of the spell is the one who chooses whether it goes on the top or bottom of their library. All players will know this information.

Subtlety's triggered ability targets a spell on the stack. It can't target creatures or planeswalkers on the battlefield.

A spell that's put into its owner's library doesn't resolve, but it isn't countered. This will work on spells that say they can't be countered.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as an evoke cost), add any cost increases, then apply any cost reductions. The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.