Am I allowed to activate an action anytime regardless of whether or not the effect can resolve? So, for example, can I sacrifice the slayers of karak kadrin regardless of whether my opponent is attacking or not?

Nope, you need a valid target.

Triggering a Card Effect (v1.7)

In order to successfully trigger a card effect, the player must declare that he is activating the card, declare targets, then pay any additional costs denoted on the card and meet any conditional requirements on the card. An easy way to identify an additional cost is the formula “Do X to do Y” in which the first part, do X, is the cost. A player cannot pay costs with cards, resources, etc., he does not control. If a player cannot fulfill these requirements to trigger a card effect, he cannot attempt to trigger it.

Thank you once again.