Once I select an Element the spell disappears without providing any benefit to the party (spell points are spent).

I believe some gem should light up somewhere on the screen.

Also, find an enemy that does low amounts of the damage type protected against; you should see this spell sometimes doing no damage (gem below the character will remain green). Note that this will also prevent status ailments associated with the attack.

I think there may be some way to check what effects are active, though I don't remember if it's present in MM3 or only in the Xeen spells.

Unlike spells like Power Shield, spells like Protection from Elements will protect the entire party in MM3.

(Note that these spells will wear off at dawn (unless you skip it by entering a shop at the right time) or when you rest.

It does work, but it is not reflected in the resistances display. For example, on the Isle of Fire I would take damage by walking without the spell, but not if I have it active.

Pressing I should show active effects.

Yes, I was going by the Resistances display.

Good to know - this is reassuring.