Seyed Saied Alavi

In the name of Allah

Yes. Reciting any dua and supplication is allowed during the period.
Keep in mind that touching the sacred names of Allah, the Holy Prophet, and the Imams peace be upon them is forbidden in the state of period.
Also if the Dua contains a verse of the Holy Quran, it's okay to recite them, but be careful not to touch those words. 

WasSalaam.

In the name of Allah

Touching the words of the Quran without Wudhu or Ghusl is Haram.
However, Touching other parts of the Quran, like the cover, page margins, etc. without Wudhu or Ghusl, is not Haram, but it's Makrooh.

WasSalaam.

In the name of Allah

Such Hadith is not narrated in major Shia sources.
However, there is a similar Hadith in the more recent Shia books (like Bihar al-Anwar), narrated (without a chain) from the Prophet -peace be upon him and his Ahlul Bayt- that conveys a different meaning:

عُلَمَاءُ أُمَّتِي كَأَنْبِيَاءِ بَنِي إِسْرَائِيلَ
The Scholars of My Ummah are like the prophets of Bani-Israel.

This hadith does not state superiority, but similarity. There are different interpretations as to the meaning of this analogy and to whom the prophet is referring when he says "Scholars". 

Some experts believe that "scholars" is only referring to the Infallible Imams, and the hadith means that the Imams are Hujjah (Proofs of Allah) to the people, just as those prophets were Hujjah to the people of their time.
Other experts expand the meaning to non-infallible scholars and belive the hadith is stating that just as those prophets were guardians of their people's faith and beliefs, Islamic scholars will guard and preserve the religiosity and beliefs of the Muslim community.

The abovementioned Hadith is narrated in:
Bihar al-Anwar - v2, p22
Mustadrak ul-Wasail - v17, p320

WasSalaam.

In the name of Allah

Their permission is not needed in this case.
However, it behoves a Muslim to be respectful towards the parents. So try to get them on board if possible.

WasSalaam.

In the name of Allah

Provided that these socks (1) Won't attract the attention of Non-mahram and (2) Do not qualify as Zinah (adornment), they CAN be considered as proper cover for the feet. Otherwise wearing them is in contrast with the meaning and the purpose of Hijab.

WasSalaam.

In the name of Allah

During the 9 years of The Holy Prophet's life after Hijrah - depending on the definition of battle - between 80 to 100 counts of Battle between Muslims and non-muslims are recorded in history. 
The Holy Prophet -Peace be upon him and his Ahlul Bayt- was personally present and leading the Army in 27 of these Battles that are called Ghazwah (غزوة). The rest were lead by his appointed generals.
It's worth mentioning that most of these battles were resolved without any/major conflict like the Conquest of Mecca.

Here you can read more details about some of these battles:
https://www.al-islam.org/life-muhammad-prophet-sayyid-saeed-akhtar-rizvi...

WasSalaam.

In the name of Allah

The answer is Yes.

When You breastfeed someone else's child (with all the conditions that will be mentioned below) That child is basically like a child of Your own. So he/she will be Mahram to:

• You (Breastfeeding mother), your parents, your grandparents and so on, your siblings, your aunts and uncles.
• Your husband (Breastfeeding Father), his parents, his grandparents and so on, his siblings, his aunts and uncles.
• Your Children (current and future), your grandchildren and so on.

But what are the conditions for breastfeeding to result in Mharamiyyat?

1. The child should suck the milk from the breast. So if the milk is poured into the child's mouth, it doesn't count.

2. The child should be under two years of age.

3. The milk should be the result of a Halal relationship.

4. The Child should not throw up the milk. If so, it doesn't count.

5. The quantity or duration of breastfeeding should be either of these:

• Enough so that his/her body would grow due to that milk.
  (Grow: muscles/meat are created or bones will be strengthened)
• 15 times in a row. (without any other food or milk from another woman)
• 24 hours straight. (without any other food or milk from another woman)
   

WasSalaam.

In the name of Allah

Considering the obligatory Qurbani (sacrificing sheep, goat, etc.) for a Haji (Pilgram to Makkah) in the Hajj al-Tamattu on the Day of Eid al-Adha, every Haji should offer One Qurbani and not less. so sharing it with another Haji won't work.

However, for a Mustahab (recommended) Qurbani, any number of people can contribute and share the Thawab of one Qurbani.

WasSalaam.

In the name of Allah

Yes, She is not one of your Maharim, therefore it's permissible for you to marry her.

Wassalam.