If a ship meets the requirements of Fearlessness for a Cluster Missile shot, does the attacker get to add the extra die result for both attacks of the Cluster Missile?

The changes to TLT + Tactician have me a little confused on if this works or not. I know that Tactician triggers AFTER the attack, so it only has one opportunity to trigger as the attack technically never ends, whereas 2 different attacks still happen, so Fearlessness should be able to trigger still.

Is that correct?

Yes. Effects that modify dice happen during the appropriate Modify Dice steps in the attack sequence unless otherwise specified, and those happen twice during "perform this attack twice" attacks.

Yup. I'd agree you can use it. It's a "when attacking" trigger, and not limited to once a round or anything.