You need a subject in the first one. Who or what can't wait?

It’s wrong because there is no subject. And ‘debut’ is a noun or a verb, not an adjective. So you’ve made up a noun phrase, ‘debut game’ which is understandable but not natural. Examples: He did well in his debut. He went 2 for 4. I’ve bought tickets for his major league debut. He debuts with the Yankees next week. I can’t wait. In general, ‘debut’ as either noun or verb isn’t that common a word. It’s fairly highbrow from French. As a lower level speaker you would risk not being understood. More natural would be to use a standard adjective: ‘I can’t wait for his first game.’ That’s something anyone could say.

Yes, it sounds natural. Here’s a slightly refined version for clarity: "Can't wait for his debut game. He’s a player." Thanks in advance!!!

Would you mind taking turns dumping the trash? I feel a little hard done by.

1. Good. 2. Just as I left home. 3. I went for a walk. 4. Raining