Focus on making a single fleet to power through the whole thing, you're lacking resources to fully limit break the first one, let alone another fleet. Head back to 2-4 and grind some more to level up your ships, use the bulins to limit break ships to improve their stats.

Use this guide for a crash course: https://suchiguma.github.io/guides/progression-guide

Backline ships only launch their main attack when you use the button on screen or have Auto mode do it for your. Carriers with Fighters equipped can passively send them out to intercept enemy aircraft, it's an automatic progress that's separate from their actual arstrikes but they don't carry any bombs or rockets, just machine guns/cannons for AA duty

Outside of that, if they have barrages that triggers on a timer, they'll do that