Removing a shield counter when a permanent would be dealt damage or destroyed isn’t the same as regenerating a creature.

“Shield” is not an ability that creatures have and shield counters are not keyword counters. If a creature with a shield counter loses its abilities, the shield counter will still protect it as normal.

Shield counters don’t prevent players from sacrificing creatures.

If a permanent that would be dealt damage has more than one shield counter on it, that damage is prevented and only one shield counter is removed.

If an Aura is put onto the battlefield without being cast, the Aura’s controller-to-be chooses what it will enchant as it comes back onto the battlefield. An Aura put onto the battlefield this way doesn’t target anything (so it could be attached to an opponent’s permanent with hexproof, for example), but the Aura’s enchant ability restricts what it can be attached to. If the Aura can’t legally be attached to anything, it remains in its current zone.

A creature with a shield counter on it may still be destroyed by state-based actions if it has damage marked on it equal to its toughness or has been dealt unpreventable damage by a source with deathtouch.

If a permanent with a shield counter is dealt unpreventable damage, that damage will be dealt and a shield counter will still be removed.