Will countering a spell that left the stack still trigger abilities?
Baral will trigger once. You cannot counter the same spell more than once.
As you already quoted the relevant rule 701.5a, countering a spell or ability means to remove it from the stack:

701.5. Counter
701.5a To counter a spell or ability means to cancel it, removing it from the stack. It doesn’t resolve and none of its effects occur. A countered spell is put into its owner’s graveyard.

Since spells can only exist on the stack, a countered spell will stop being a spell, and will no longer be a valid target for counter effects.

111.1. A spell is a card on the stack. As the first step of being cast (see rule 601, “Casting Spells”), the card becomes a spell and is moved to the top of the stack from the zone it was in, which is usually its owner’s hand. (See rule 405, “Stack.”) A spell remains on the stack as a spell until it resolves (see rule 608, “Resolving Spells and Abilities”), is countered (see rule 701.5), or otherwise leaves the stack. For more information, see section 6, “Spells, Abilities, and Effects.”

If you choose the counter option of Mystic Confluence three times, Mystic Confluence effectively reads:

Counter target spell unless its controller pays 3.
Counter target spell unless its controller pays 3.
Counter target spell unless its controller pays 3.

When Mystic Confluence resolves and the first ability already counters the targeted spell, that spell will immediately be removed from the stack and Baral will trigger. The second and third part of Mystic Confluence lack a valid target, and will not do anything.