QIf I play this spell with a Spellchain of 15, does it deal 3 damage to all enemy followers on the field?

AYes. If the condition Spellchain (15) is fulfilled, the effect "deal 1 damage to each enemy follower on the field" is applied 3 times, dealing 3 separate instances of 1 damage for a total of 3 damage.

QMy opponent has Elios, Loyal Dragoon on their field, whose ability triggers whenever it takes damage. If I play this spell with a Spellchain of 15, how many times does Elios's ability trigger?

AIt triggers 3 times.