All of these say approximately the same thing, with subtle differences. "She's fit for that role" and "she's suitable for that role" are equivalent; both imply that she has the necessary qualities to perform the role, irrespective of her actually performing it or not. The only tense information in the sentence is contained in "she is," which tells us she has those qualities currently.
"She'll fit in that role" suggests that she is being or has been cast for the role and will perform it in the future. "She suits that role" suggests that she is already performing the role.
The similar "she would fit in that role" or "she would suit that role" suggest, like the versatile case above, that she is inherently qualified for the role, but exclude the case where she is already performing it.
The differences all come down to verb tense. Sentence (3) is in the simple future tense, (4) is in the simple present tense, (5) and (6) use the subjunctive mood, and (1) and (2) use only an adjective phrase.