Does Brynhildr Thundersong's ability resolve if he Star-Crossed is used in reaction to his ability? Does his ability still resolve?

Yes, Brynhir Thundersong's triggered ability will still resolve even if he is returned to your hand by Star-Crossed after the ability has been placed on the chain.

According to the rules of Riftbound and FAQ regarding Brynhir Thundersong, once a triggered ability is on the chain, it is independent of the unit that created it.

The Sequence of Events:

1. You play Brynhir Thundersong: She resolves and enters the battlefield. Her "When you play me" ability is placed on the chain.
2. Opponent plays Star-Crossed in reaction: They add Star-Crossed to the top of the chain, targeting Brynhir and one of their own units.
3. Resolution (LIFO - Last-In, First-Out):
   • Step 1: Star-Crossed resolves first. Brynhir is returned to your hand.
   • Step 2: Brynhir's "When you play me" triggered ability resolves next.

Why the ability still resolves:

As established in RiftJudge FAQ #9750 and Rule 392, abilities do not "fizzle" or stop functioning just because the source unit has left the battlefield. Once the ability is on the chain, it will execute its effects regardless of whether the unit is still in play, provided the ability's instructions can still be followed. Since Brynhir's ability is a global effect ("opponents can't play cards this turn"), it does not rely on her presence on the board to resolve or to function for the remainder of the turn.

Note: This interpretation is based on the standard chain resolution rules and existing FAQs regarding Brynhir Thundersong and the independence of chain items.