Marc,
the third version is done by adding the brim to the cap.
From what I gather, the brim is included in the kit.
There are a few options, depending on what you add or leave off the bust; all are included in the kit.
The peak (visor) is indeed included in the kit as a separate part. It's up to the modeller to use it or leave it off.
Most of the fur headresses of the period were merely 'commercial' wool caps (with or without peak) wrapped with fur. Coon skin hats à la Davy Crockett were rarely (or not at all) seen in contemporary descriptions or drawings.
The decorative badger skull comes from a painting by Frank McCarthy whose depictions of the Mountain Men are IMO by far the most inspiring.
The characteristic heart-shaped pipe holder is a small leather pouch called 'gage d'amour' (love token) manufactured and given to the trapper by his native wife (wives ).