When I cast Simulacrum to make a copy of a creature with a feature like Rangers Companion, do I get a free animal companion to go with it?

The Simulacrum spell contains an interesting clause.

It appears to be the same as the original, but it has half the creature’s hit point maximum and is formed without any Equipment. Otherwise, the Illusion uses all the Statistics of the creature it duplicates.

Since the Companion feature is part of a creatures statistics, this means that it should get duplicated, I think. So if I were to duplicate a creature that has a feature like Rangers Companion (or something similar), does the animal companion automatically come with it?

Related questions that would have an answer based on the answer to the primary question:

  • If we don’t get a free companion, can the simulacra bond with a new one?

  • If we do get one, would it also be an illusion, or is it a real flesh-and-blood creature?

  • If the Simulacra dies, does the companion instantly die as well?

  • If the companion dies, can the Simulacra bond with a new companion?