1. My opponent controls a Planeswalker and uses its ability. End of turn.
2. I play In Bolas's Clutches and target that Planeswalker. It comes under my control (right?).
3. Can I now use this Planeswalker's ability or do I have to wait another round because its ability was already used this round by my opponent? (by round I mean two turns)

In Bolas's Clutches

Types: Legendary Enchantment — Aura Card
Text: Enchant permanent / You control enchanted permanent. / Enchanted permanent is legendary.