Proud Pack-Rhino

"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.

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

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

You don't have to choose every permanent or player that has a counter—only the ones you want to add counters to. Since "any number" includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.

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.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.