Welcome back, Hela.
Semantically, 'take advantage of' is synonymous with exploit and the euphemism seduce. Structurally, it's phrasal-like; a verb that takes a noun phrase as its object:
[VPtake [NPadvantage of Max]]
[VPtake [NP[ADJunfair [Nadvantage]] of Max]]
In passive voice, the object of the preposition functions as the structural subject,
Max took advantage of John.
John was taken advantage of.
A: I heard someone say John was taken advantage of? Is that true?
B: Who was taken advantage of?
A: I heard that John was. Do you know if it's true?
If the culprit;e.g., Max, is unknown or the speaker feels uneasy about stating exactly who the culprit is, the "by" phrase is omitted; if the culprit is known, active voice is the norm.
Let's get to your example sentences.
a) I consider her to have been taken unfair advantage of.
=> She's been exploited.
=> She's been seduced.
=> She's been taken unfair advantage of. (It's awkward, as is a) )
b) Advantage was believed to have been taken of John.
If 'take advantage of' functions as a phrasal verb (See [i] below), moving its object out of the phrase would alter the verb phrase's structural integrity and render the sentence ungrammatical, as in [ii]:
[i] Active: [VPtake [NPadvantage [pp of Max]]]
[ii] Passive: *advantage [VPwas taken [NP___ [PPof John]]
It appears the object of the preposition is free to move, but not the object of the verb. The reason being, 'taken advantage of' is a set phrase.
c) We believe advantage to have been taken of John.
=> See b) above.