Why are hashing private key in Ed22519 key generation and later the modifications required?

Question

In EdDSA with Ed25519 the algorithm of public key computing is following:

h = hash (privateKey)
h[0] &= 0xF8
h[31] &= 0x7F
h[31] |= 0x40
publicKey = h * B

The questions are

1. Why is Hashing in Ed25519 key generation needed?
2. Why are the actions on h bits are needed?
3. What does the clearing relate to the 31st bit?

Answer 1

1. Hashing in EdDSA key generation

   This is addressed in the original paper as

   Legitimate users choose $A = [a]B$, where $a$ is a random secret; the derivation of a from $H(k)$ ensures adequate randomness.

   If you don't apply the hashing, there is no problem on the verification of the signatures of such public keys.

2. The question is what actions on h bits are needed for?

   This clearly clears the lower bits so that it is a multiple of 8, and this removes the small groups on the curve that this information, although small, can leak in a small-subgroup attack. See more in this answer

3. The clearing relates to 0th bit and what about 31th?

   This is mainly due to a possible timing attack (in this site)

Stick to the advises and standards; see RFC 8709.