It is not permissible to offer an explicit proposal of marriage to a woman who is observing ‘iddah following the death of her husband or divorce
What we understand from your question is that your aunt’s divorce from her husband has not yet been completed, because you say “the official talaaq procedure is still not finished”. If that is the case, then your aunt is still married to her husband, so it is not permissible for anyone to propose marriage to her or to make an agreement with her to get married after her divorce, until the divorce has actually been completed.
If the divorce has been completed but it is a revocable divorce (first or second talaaq), then it is also not permissible during the ‘iddah period for anyone to propose marriage to her, either explicitly or implicitly, because the woman who has been divorced revocably still comes under the same rulings as a wife, and her husband has the right to take her back at any time he wants, so long as the ‘iddah has not ended.
But if the divorce is not revocable (such as a third talaaq or talaaq in return for some compensation paid by the wife), then it is permissible to hint at a proposal during the ‘iddah, but it is not permissible to propose explicitly, because Allaah says (interpretation of the meaning):
“And there is no sin on you if you make a hint of betrothal or conceal it in yourself”
This verse speaks of a woman who is observing ‘iddah following the death of her husband, but by analogy the scholars applied it to everyone who is observing ‘iddah and has no way of going back to her husband.
The different between an explicit proposal and an implicit one is that an explicit proposal is worded in such a way that it cannot mean anything but marriage, such as “I want to marry you” or “I will propose to you” etc.
As for the implicit proposal, it is worded in such a way that it may mean marriage or something else, such as “I am looking for a wife” and so on.
It is well known that people use the expression “reciting al-Fatihah” to refer to an explicit proposal. Based on this it is not permissible for anyone to propose to your aunt and recite a-Faatihah or for her to sit with him until the 'iddah has ended.
It should also be noted that reciting al-Faatihah at the time of engagement or marriage is not mentioned in the Sunnah.
The standing Committee for Issuing Fatwas was asked: Is reciting al-Faatihah when a man proposes marriage to a woman an innovation (bid’ah)?
Reciting al-Faatihah when a man proposes marriage to a woman or when doing the marriage contract with her is an innovation. End quote.
Fataawa al-Lajnah al-Daa’imah (19/146)
See: al-Sharh al-Mumti’ (10/124-127); al-Mawsoo’ah al-Fiqhiyyah (19/191).
And Allaah knows best.