You cannot cast Smell Fear without any targets just to proliferate. You must choose at least one creature you control as a target to cast this spell. If you don't choose a creature you don't control as a target, no fight will occur.

If you choose two creatures as targets with this spell and only one target is legal as the spell resolves, no fight will occur and no damage will be dealt, but you will still proliferate.

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.

To proliferate, you can choose any permanent that has a counter, including ones controlled by opponents, and you can choose any player who has a counter, including opponents. You can't choose cards in any zone other than the battlefield, even if they have counters on them.

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.

If all targets are illegal as Smell Fear tries to resolve, it doesn't resolve and you will not proliferate.