Sunni-Shi'a

Omar was the first who forbade Mut’ah marriage, not the Prophet (SAWA).

Omar said in public during his rule: Two Mut’a were allowed during the era of the Prophet and I stop it and will punish on it, the Mut’ah marriage and Mut’ah of Hajj. ( 1.Musnad Ahmad Ibn Hanbal , v. 22, p. 365, Hadeeth 14479.
2. Al-Sarkhasi in al-Mabsoot, v. 4, p.27.
3. Ibn Baaz, the grand WAhabi Mufti in Majmoo’ al-Fataawa , v. 20, p.298.
4. Ibn Hazm in al-Muhalla , v. 7, p.107.
5. Sunan al-Nasaa’ee in al-Sunan al-Sughra H. 2735 and al-Sunan al-Kubra H. 3716.
6. Ibn Taymiyyah in Kitab al-Taharah wal Hajj, v. 2, p.471 and many others.)

Omar never said that Mut’ah marriage is forbidden and that he forbids people for it because it is forbidden in Islam, but rather the exact opposite. He affirmed that it was allowed during the era of the Messenger of God (Peace and Blessing be on him and his Progeny ) and he (Omar) who wants to prohibit and punish against it. The evidence is crystal clear that the Mut’ah marriage was allowed and been practiced by Muslims during the era of the Messenger of God (SAWA) and during the era of the Abu Bakr government and part of the era of the Omar government, and confirms that the first one who forbade it is Omar.
On the authority of Abu Nadhra, he said: (I was with Jabir bin Abdullah, a man came to him and said: Ibn Abbas and Ibn Al-Zubayr differed concerning the Mut’ah marriage and Mut’ah in Hajj, so Jaber said: We did them with the Messenger of God (may God’s Salutations and peace be upon him and his Progeny)), then Omar prohibited them, so we did not modify them (Sahih Muslim / c 4 p. 59 - Sunan Al-Bayhaqi / 7 p. 206).
This hadith was narrated in another form: (On the authority of Abu Nadhra on the authority of Jaber (may God be pleased with him) he said: I said that Ibn al-Zubayr forbids Mut’ah marriage and that Ibn Abbas orders it. He said: On my hand the conversation took place, we did Mut’ah marriage during the time of the Messenger of God (may God’s Salutations and peace be upon him and his Progeny) and with Abu Bakr. When Omar took the government over, he addressed people and said: This is the Messenger of God, and the Qur’an is this Qur’an, and Muslims were doing Mut’ah marriage during the time of the Messenger of God (may God’s Salutations and peace be upon him and his Progeny) and I have banned them and admonish them: one of them The Mut’ah marriage, and I will not find a man who married a woman for a period, but will throw him with stones, and the other: the Mut’ah of Hajj (Sunan Al-Bayhaqi / 7 p. 206).
It was also narrated in a third way: (On the authority of Jabir bin Abdullah, he said: We did Mut’ah during the era of the Prophet (may God’s Salutations and peace be upon him and his Progeny): Hajj and women, and Omar forbade them. (It was included by Ahmad Ibn Hanbal in his Musnad C 3 / pp. 356-363) in two ways, one of which is the way of Asim . It is authentic Hadeeth as the narrators men are all confident.
And on the authority of Omar, he said in his sermon: Two things that were in the era of the Messenger of God (may God’s prayers and peace be upon him), and I finished them and punished them: the Mut’ah of Hajj and the Mut’ah of women. (The provisions of the Qur’an for Al-Qassas, Part 1/352 and Part 2, p. 191, Tafseer Al-Qurtubi 2, p. 392).
Al-Ragheb said in his book  (Al-Muhadharaat 2, p. 94): Yahya bin Aktham told a sheikh in Basra: Whom did you follow in the permissibility of Mut’ah marriage ? He said : My evidence is from Umar ibn Al-Khattab. He said how come when Umar was the most against it ?! He said because the authentic narration is that he ascended the podium and said: God and His Messenger have given you two Mut’ah, and I am forbidding them on you and punishing on them, so we accepted his statement that it was on the time of the Prophet, and did not accept his prohibition.
These Hadeeths and others indicate a personal opinion of Umar against what was been practiced during the time of the Messenger of God (may God bless him and his family and peace) and even the time of Abu Bakr !!
Some apologized for him that he was very hard on the issue of Mut’ah marriage because he entered a day in the house of his sister ‘Afra, and found in her lap a baby who had been bron from Mut’ah marriage, so Omar got angry and went out to the mosque and went up the pulpit and prohibited Mut’ah marriage.
Abdullah bin Abbas, the well known companion and cousin brother of The Prophet Muhammad (SAWA) confirmed that the prohibition of Mut’ah marriage came only from Omar, and it was reported that Ibn Abbas said: The verse of Mut’ah marriage is very clear in Quran, and it is as it was , it has never been abrogated. (See Al-Ghadeer, Vol. 6, p. 210).
Wassalam.

You do not need permission from any one for such operation, but you need to be sure that it is reversible vasectomy.

Wassalam.

1. Going for Hajj with Sunni Muslims does not harm your Hajj as far as you perform the Hajj in the proper way according to the Prophet (SAWA) and Ahlul Bayt (AS). You need to read a book of Hajj steps according to Ahlul Bayt (AS) or to contact Shi'a scholars how can guide you.

2. Going for Hajj on behalf of a Sunni deceased person is allowed if you have already performed you own obligatory Hajj, or if Hajj is not yet obligatory on you because you can't afford it.

Wassalam.

Not at all. Such narrations which contradict with Quran are fabricated and have no value whatsoever among the followers of Ahlul Bayt (AS).

Allah (SWT) Has ordered people to follow the prophets ( We have never sent any messenger but to be obeyed by Allah's order) 4:64. All the prophets are infallible and never committed any sinful act. 
We find in Bukhari many narrations which go against Quranic facts and we have no way to leave Quran for the sake of Bukhari or any one else.

Wassalam.