Prosperous Bandit

If the spell is countered, the offspring ability will not trigger, and no token will be created.

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.

In the rare case where the creature doesn't have the offspring ability when it enters, the ability won't trigger even if you paid the offspring cost.

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.