I mostly read it in older works. Can I treat it like a regular word, and what would spito, spita, spiti etc mean?
The definition of spiti in the Plena Ilustrita Vortaro is
Montri al iu, ke oni plezuras, kontraŭstarante al lia/ŝia volo, aŭ ke oni estas preta batali
To show another person that one takes pleasure in opposing their will, or that one is ready to fight
Spite on its own means something between "defiantly" and "spitefully". Spite de means "in spite of" when you want to imply that literal defiance is involved, or at very least a certain amount of cosmic irony, in contrast to malgraŭ which just means "despite" in its normal usage as a dead metaphor. Spite ke means "in spite of the fact that" and pairs with malgraŭ ke.