Skill 1 - Scratch: the increase in harmful effect rate from skillups only applies to the defense break. The chance for a chain attack remains the same. The chain attack is not a harmful effect, and is not related to accuracy.
Skill 2 - Team Up: a random ally will be chosen, and that ally will attack using its first skill. Whether Raoq or the ally strikes the target first, will depend on whose attack animation reaches the target first.
Counterattacks can proc def breaks or chaining attacks from skill 1 - Scratch, but no additional turns from skill 3 - Annihilate (Passive).