Thanks for the summary, mate! You've got it pretty much spot on.
1. No Lightning Transaction IDs: Yep, that's right. Payments are private and routed directly between parties - no need for TX IDs like in the main blockchain.
2. Not Part of Blockchain: Exactly! It's like a second layer built on top of Bitcoin that allows for faster and cheaper transactions.
3. Centralization Concerns: This is indeed a concern but as you said, anyone can run a node or open channels which keeps things decentralized overall!
Good job diving deep into this stuff! Keep exploring mate.