【Chain】 is an effect that activates following the effect written above it if the symbol specified as a condition by that 【Chain】 effect is on your field.

No, it does not. The 【Chain】 effect activates immediately following the effect written above it. In addition, if another effect (for instance, a When Destroyed effect) occurs as a result of the effect written above the 【Chain】 effect, the 【Chain】 effect will activate first.

Yes, it can. For example, if an effect instructs you to select one of your opponent's spirits and exhaust it, the 【Chain】 effect can be activated if its conditions are fulfilled even when your opponent has no spirits.