How does Jigglypuff's Rest work?

In Super Smash Brothers Melee (SSBM), Jigglypuff from the Pokémon franchise is a playable character. Her down special move is Rest which causes her to flash then fall asleep. To the uninitiated, this move seems useless. Please explain this move.

How many frames is the offensive part active?

This is particularly important in team battles or with the presence of Propeller Shy Guys, the active frames of the offence seems to be extended during a successful strike. How does this work?

Does the offence activate at the same speed as a shine?

In particular, why do competitive players prefer hitting with the move during a short-hop?

Rest hits on frame 1 and only frame 1, which I believe is the same as the shine. Jigglypuff is intangible for the first 26 frames of the move. (source)

Competitive players like to hit during a short hop because characters do not push away from each other when in the air, which makes the hitbox easier to nail (given it's in the center of Jigglypuff's body and only about the size of its eye).

When moves hit things, they go through an amount of freeze frames. This causes both the attacker and the target to freeze in their current state for an amount of frames based on the damage of the hit, which can cause hitboxes to last longer. In the case of Rest this could possibly make it easier to hit, but given the size of the hitbox I don't think people seriously try to do it unless the Guy is in the same place as the opponent.