Should Evelynn always one-shot, or should she sometimes mainly make the whole map play under threat?

The most reliable build on Evelynn is the one that preserves the first spike while still keeping an escape valve. If your item order prevents you from playing the champion's first real window, the build may look strong on paper but it is not reliable.

When should Evelynn be avoided, or at least have her standard deletion build slowed down?

You should adapt as soon as the enemy draft stops you from playing the timing the build was meant to serve. If you need to survive longer, absorb more poke, or answer a specific engage pattern, the purchase order must move before you even think about the final six-slot build.

What is Evelynn's true main spike when the game is mainly won through vision fear and side lanes?

Stasis is usually the most stable choice because it protects the exact moment when Evelynn takes the most risk. Change it only when another enchant answers the lobby's concrete problem more directly.