Unbounded Potential

You don't have to choose every permanent or player that has a counter, only the ones you want to add another counter 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.

While proliferating, if you choose a permanent or player with multiple kinds of counters, the permanent or player gets another counter of each kind, not just one kind. This change from the original proliferate rules was introduced in a previous set.

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.