Do you believe the reports that Ahmed married Kosem? We know she his favorite consort among six women in his harem. However, it's debatable if she was his legal wife? Hurrem, Nurbanu, Safiye, and Telli Humasah were all confirmed as wives. Did Mehmed also marry Gulnus? I can't remember?
Personally? I don't think so. The big champion of this theory is Özlem Kumrular who, in her book Kösem Sultan: İktidar Hırs ve Entrika, dedicates a paragraph to this.
Quoting it all would be just too long so I'm going to make a summary of her theory.
She starts by saying something that is very true:
None of the Ottoman sources available to us say that Ahmed married Kösem. As it has already been mentioned, for obvious reasons, except in exceptional circumstances, the sultans did not marry their women. Foreign sources do not mention the wedding, but treat Kösem as Ahmed's wife and leave the matter unsolved. For example, in 1609, the Venetian Ambassador Bon says that Ahmed had four children with his three kadıns, but that he was not married to any of them. However, Knolles is of the opinion that Ahmed married Kösem.
I'm not sure Knolles can be trusted, because he's not exactly the most accurate author ever, but she doesn't mention a particular book or page so I don't know exactly what he said.
In any case, she goes on saying that she found a document in the Venetian State Archive - which I found too but it's in Ottoman Turkish so I can't read it, I can only look at it - which would prove, according to her, that Kösem was Ahmed I's wedded wife.
The document is a letter that the Ottoman court sent to Venice to announce Murad IV's accession to the throne. In it the author (who? we'll see that below) writes about Kösem like this:
"Her Majesty the Sultana Valide [...] for the late Sultan Ahmed, whom Allah took with him, was a very important person and he loved her so much that he honored her by marrying her."
The letter is also interesting because it says that "apart from the new padişah, two little sons of Kösem, Selim and Orhan, were still alive". I won't dwell on this because it is not the topic of your ask. I'll just say that we don't know who Selim and Orhan are.
Now, back to the wedding.
Kumrular alleges that Kösem may have written (dictated, of course) that letter herself to strengthen her role as regent:
Let us not forget that in the case of the European queens of the time, who ruled on behalf of their sons or husbands, the fact that they were lawful wives was of considerable importance. During this period, as in almost all centuries, the wedding was an important source of her legal status for a woman. It is obvious that Kösem, to a state as important as Venice, wanted to legitimize her position. Emphasizing that she was the wife of the deceased ruler and praising her were aimed at elevating her in relations with the Venetian state, gaining respect for her and obedience to her words.
And this is where I start having problems with her theory. While the institution of the regency in the Ottoman empire was basically new, the Venetians were well aware that sultans did not get married, and they were used to the valide sultans not being wedded wives. In fact, after the death of the sultan, his consort who became valide sultan also became a free woman. She was not a slave anymore so that she had not been a wedded wife is of no consequence. She derived her power from her son and not from the dead sultan.
So I don't understand why Kösem would feel the need to highlight that she was Ahmed I's wedded wife. Also, second question: what words did she (or whoever wrote the letter) exactly use to say "wedded wife"? Unfortunately, Kumrular doesn't say. I think that a linguistic analysis of the letter would have been interesting, especially because I don't think there are a lot of people that can read Ottoman Turkish.
On the other hand, Venice's reply to this letter convinces us that Kösem was right to attach such importance to it.
Really? What does the answer say? Who knows, Kumrular doesn't say.
If it was really the Sultana who commissioned this letter to be written, I don't think she would dare to risk that much and take responsibility for such a serious lie just to sanction her rights. Venice knew the Ottomans' every move, followed their every breath, so it wouldn't have taken long for them to prove that the content of this letter was a lie.
Really? [2] I have doubts.
Therefore, we can believe that Kösem was really the wedded wife of Sultan Ahmed.
Really? [3] I have doubts. [2]
In sum, I feel like her reasoning is a little flawed. Of course, some things may be lost in translation but I don't know... Personally, I'm not as sure as she is that there was an official wedding.
As for your last question: no, Mehmed IV did not marry Emetullah Râbia Gülnûş.
This is what the quotes that you paraphrased actually say (it is always important to look at exact quotes in history):
"[a woman of] beauty and shrewdness, and furthermore ... of many talents, she sings excellently, whence she continues to be extremely well loved by the king.... Not that she is respected by all, but she is listened to in some matters and is the favorite of the king, who wants her beside him continually. . . " — Leslie P. Peirce, The Imperial Harem: Women and Sovereignty in the Ottoman Empire
and
"she can do what she wishes with the King and possesses his heart absolutely, nor is anything ever denied to her." Contarini noted, however, that Kosem "restrains herself with great wisdom from speaking [to the sultan] too frequently of serious matters and affairs of state." — Leslie P. Peirce, The Imperial Harem: Women and Sovereignty in the Ottoman Empire
First quote is by Contarini in 1612, the second quote is by Valier in 1616.
So, what the Venetian ambassadors say is that Kösem knew Ahmed's nature very well: she knew that he hated women's interferences and that probably pressuring him too much would turn against her.
As you said, it is possible that she used her sassy personality to keep things "light" with him. Contrary to his depiction in MC:K, Ahmed was quite rigorous and conservative (remember Safiye's poor organ? Yeah...)
