Intrepid Rabbit

The token created by the offspring ability isn’t “cast”, so abilities that trigger when a creature spell is cast won’t trigger for the copy.

If the spell resolves but the creature with offspring leaves the battlefield before the offspring ability resolves, you’ll still create a token copy of it.

Any “enters” abilities of the copied creature will trigger when the token enters. Any “as [this creature] enters” or “[this creature] enters with” abilities of the copied creature will also work.

You can pay an offspring cost only once as you cast a spell with offspring. You can’t try to pay it multiple times to get more token copies.

The token copies exactly what was printed on the original creature and nothing else, except it’s a 1/1 (unless that creature is copying something else; see below). It doesn’t copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its types, color, or so on.

In the rare case where the original creature is copying something else when the offspring ability resolves, the token enters as whatever that creature copied, except it’s a 1/1.