So, the bit about countering the Periculum spell isn't something I recall from the books, but there's definitely a logic to it in-universe. Periculum shoots red sparks, right? It's meant as a signal, a distress flare. In a duel, you'd probably counter it the same way you'd counter any jet of magical energy—with a Shield Charm, 'Protego'. I'm not sure it would even be worth countering offensively, since it's not an attack spell. The real trick would be stopping your opponent from casting it if they're trying to call for backup, so maybe a quick 'Expelliarmus' or a silencing charm would be the proactive 'counter'.
Thinking about it, the magic in those books often follows intent. A spell designed for communication might be harder to magically 'negate' than one designed to harm, because the magic itself is less forceful. I'd be more curious if there's an established counter-charm in any supplementary material, like 'Finite Incantatem' to just end its effects. Without a canon answer, it's all speculation, which is half the fun of these discussions anyway. The sparks probably just fizzle out on their own after a bit.