This is the "Well World" series by Jack L. Chalker. The characters are teleported to the "Well World", which is, among other things, kind of a proving ground for a super advanced race to create new species. The world was divided into "hexes" and each race had its own hex. When the main characters get to the world, they go through a thing called "the Gate" where they are transformed into a new species (the characters don't really take the new form over; they become them). The characters are also transported to the "Hex" that their new species originates from.
The plant creature is in the first book, "Midnight at the Well of Souls". The faun and the woman (Mavera Chang) are from the second and third books, "Exiles at the Well of Souls" and "Quest for the Well of Souls".
Here is a link to the appropriate Wikipedia for the author, with sublinks to the books. Here is the direct link to the series.
Here is the cover of the first book.
And here's a picture of the faun creature (second book).