Hi Niels,
Top-posting because I think all questions are quite related. Ultimately, what we need is for each signature that appears in a leaf to be verifiable without any further information. Otherwise, a monitor cannot distinguish between a leaf that was fabricated by the log and an actual signature operation by someone.
1. Removing checksum: this leaves a monitor with a 64-byte Ed25519 signature. In other words, the bytes that were signed would be missing completely. 2. Permitting SHA-512 while storing SHA-256(M) as checksum: this leaves a monitor with a 64-byte Ed25519 signature and a 32-byte checksum that is unrelated to signature verification.
Let me know if this context did not answer all of your questions, in which case I will take a stab at them more explicitly in a follow-up email.
-Rasmus