If you don't put the top card of your library into your hand, you put it back on top of your library without revealing it. You'll draw it in that turn's draw step.

To determine the total cost of a spell, start with the mana cost or alternative cost you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.

If you somehow control a Herald's Horn with no chosen creature type, no spells will cost less to cast, not even creature spells with no creature type. You'll be able to look at the top card of your library at the beginning of each of your upkeeps, but you can never put it into your hand this way, even if it's a creature card with no creature type.

The effect of Herald's Horn reduces only generic mana in a spell's cost. If that cost has no generic mana, the cost isn't reduced.