Can squadrons attack more than one target? I.e. if they're engaged with multiple squadrons, could they perform an attack on each squadron they are engaged with? and if a ship is also in range, could they attack the ship too?

Nope.

How did this question even come up?

p12 RRG, SQUADRON ACTIVATION

p2 RRG, ATTACK

Nothing there says a squadron can attack twice. So the answer is No.

The only (current) way a squadron can attack twice is through Yavaris (Neb B upgrade). It allows squadrons that are activated using a squadron command to attack twice, as long as it does not move.

Other than that, they can only perform one attack.