I had a book ages ago that was 2 volumes simply listing historical texts that mention the marriage. I wish I can find it since that is what is needed to research details. However, I just stumbled upon this book here:
http://www.almabarrah.net/files/5514/7665/3429/aum_kalthoom_.pdfThe above book refutes ten Shia books that were authored to cast doubts on the Mutawatir marriage. I hope it'll save me the time of looking for the other book I had.
I will try to quickly translate some info for your benefit regarding Umm Kulthum.
She was born in the Prophet's (saw) time, at around the 6th year AH.
She married `Umar at the age of 10, in the year 17 AH. After him, she married `Awn, Muhammad and `Abdullah the sons of Ja`far respectively.
She gave birth to Zayd son of `Umar by consensus and a girl called Ruqayyah. As for her other marriages, she only had a daughter from Muhammad bin Ja`far.
Zayd died before reaching 30, he lived till after 47 AH.
As for Ruqayyah, she is said to marry Ibrahim bin Nu`aym and bore him a daughter.
Several narrations and stories about her were recorded in the books, at one point she interceded on behalf of `Abdullah bin `Umar when he refused `Ali's proposal to become his governor. In another report she gets angry when Ka`b al Ahbar insults her husband `Umar. In another she complains about the time of the Fajr prayer when she says: "My husband, the commander of faithful was killed at the time of the morning prayer and so was my father."
As for the authentic narrations, the Sahih from Zayn-ul-`Abidin mentions how after the marriage `Umar was congratulated by a group of Companions and then he mentions to them the virtue and honor of marrying into the Prophet's (saw) family.
Second authentic narration is by al-Baqir with three different chains, `Umar requests to marry her but `Ali replied: "I have reserved my daughters for Ja`far's children." `Umar insists: "O `Ali, grant me her marriage as nobody intends to be a better companion to her than I do." `Ali said: "I have (married her to you)."
In one of his narrations, it is highlighted:
تزوج عمر بن الخطاب أم كلثوم بنت علي بن أبي طالب، وهي جارية
تلعب مع الجواري،
He married her while she was a kid still playing with other children.
In one narration, `Ali says she is still young before he mentions that he reserved her for Ja`far's children.
In the narration of al-Hasan's children, `Ali sends his two sons to accompany her to `Umar.
فقال علي
للحسن، والحسين: »زوجا عمكما
`Ali told the two (Hasan & Husayn): "Go and marry her off to your uncle (i.e `Umar)."
As for the report where she is kissed, it seems to be from the weak ones. As this is a detail not mentioned in all authentic reports listed above to Zayn al-`Abidin & al-Baqir. It seems only a man called Ibrahim bin Mihran bin Rustum narrated these odd additions to the authentic stories and he is extremely weak.
In another narration by the great grandson of Ibn `Umar, he says that `Ali consulted Fatimah's children before marrying her daughter, they said: "Grant him the marriage." So `Ali sent her to `Umar and told her to tell `Umar: "My father sends his regards and says: We have fulfilled your wish O `Umar." So upon hearing this, `Umar hugged her and said: "Her father married her off to me!"
(Notice this happened AFTER the marriage was approved.)
As for the narration that mentions exposing/grabbing her leg, the authentic one was by Ibn `Uyaynah from al-Baqir, it states:
فان رضيت فهي امرأت
`Ali tells `Umar that he accepts to marry her to him, but insists that `Umar should see her first, he tells `Umar: "I'll send her to you, if you are pleased then she is your wife."
So, `Umar upon seeing her is pleased and accepts. Then he grabs her leg after she's become his wife.
فمازحها
In another report, it describes this as "So he (i.e `Umar) joked with her." By this they mean grabbing the leg and she was a kid.
In the authentic report by al-A`mash:
سوف أرسلها، ف ن رضيت فهي امرأتك، وقد أنكحتك، فزينها وأرسل
بها
`Ali tells him along the lines of the above: "I shall send her, if you accept her then she is your wife as I have married her off to you." `Ali then asked them to dress her up and fix her up for marriage before sending her to him.
When he grabs her leg, she gets upset and says "If you weren't the commander of faithful I would have broken your nose!" SHe heads back to her father and complains: "You've sent me to a bad man?" `Ali replied:
مهلا يا بنية، فانه زوجك
"Hold on O daughter, for he is your husband."
(Notice `Ali explains that her husband had a right.)
`Ali and `Umar's acceptance is clear in multiple of the above narrations and I don't have time to translate the full reports in their details. This should satisfy your first issue about the "touching".
As for `Ali reserving his daughters for Ja`far's children, then`Ali also reserves the right to change his mind. `Umar persuaded him by telling him that he would be a good companion for his daughter and `Ali accepted.
As for the link, Hafsah was linked to the Prophet (saw) through her marriage. `Umar also wanted to marry a granddaughter to be linked with the Prophet's (saw) family directly. That's how they thought of it and the more ties of kinship the better for them in their view.
Umm Kulthoum was viewed as a daughter of the Prophet (saw) since she's his daughter's daughter. `Ali's children from Fatimah were viewed as a very special case since they were the only ones the Prophet (saw) left behind.
Regarding why didn't `Umar marry Zaynab. I'll look into that later but I thought she was already married to `Abdullah.
As for marrying into the prophetic-family, it depends on the intention. If it happens out of love and nearness to the Prophet (saw) it is surely rewarded. However, if it is done for boasting and status, then there is no reward.
As for the authenticity of the Shia narrations, Insha-Allah remind me and i'll double check for you later. I know they have at least one authentic narration about the marriage.
In the Sunni narrations, it is `Ali who marries her off, in one report he asks permission from Fatimah's children but I am skeptical of this one report. `Ali's words are detailed and clear in the Sunni reports and historical books. Twelvers invented another version to counter the popular version found in all history books (the one abt `Abbas and `Umar threatening to cut `Ali's hand off if he refuses).