A spell or ability counters a spell only if it specifically contains the word "counter" in its text. If a spell or ability you control causes all the targets of a spell to become illegal, that spell doesn't resolve but it's not countered.

The cost reduction applies only to generic mana in the cost of instant and sorcery spells you cast.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as a flashback cost), add any cost increases (such as kicker costs), then apply any cost reductions (such as that of Baral's first ability). The mana value of the spell is determined by only its mana cost, no matter what the total cost to cast that spell was.