Can I play Falling Star, pass priority, then opponent also passes priority, then I use Stupefy on the same chain?

No. Once you pass priority and your opponent also passes, both players have passed consecutively and the chain proceeds to resolve the top item (Falling Star). There is no window to insert Stupefy after that — you missed your chance.

However, you can achieve the same result by holding priority. After playing Falling Star, you control the newest item on the chain and gain priority (Rule 337.1.c.3). Since Stupefy has [Reaction], you can play it immediately onto the same chain without passing first (Falling Star → hold priority → Stupefy). Then you pass. Stupefy resolves first (newest item), then Falling Star resolves.