Sayyid

The most learned Mujahid among Shia Ulama can be known through valid witnesses of at least two of the high caliber Ulama in the Hawza who are called Ahl al-Khibra or Khubra أهل الخبرة.

It is not for any one else out of the high caliber Ulama to give witness in this matter. 
Hawza Ulama usually guide people when the need arises.

There are few high learned Mujtahids but you need two high caliber Ulama to give you their wtnisses.

Wassalam.

1. Purity of bloodline because of the connection to Lady Fatima (AS) remains with every one who has this connection whether from his Sayyed father or Sayyedah mother.

2. There is another jurisprudence rule to define the Sayyed person who will be allowed to give his obligatory Zakat or Fitra to needy Sayyed. Most of our Maraaje' of Taqleed say that the definition of Sayyed is the person who was born from Sayyed father.
These are two different issues.

Wassalam.

Bani Hashim (the family of the Prophet) are entitled to Sahm Sadat if they are poor. The grand children of Ameerul Mo'mineen Ali (AS) are called Alawi Sadat while grandchildren of Aqeel ibn aabi Talib are called Aqeeli Sadat and grandchildren of Jafar ibn Abi Talib are called Jafari Sadat.

Wassalam.

When your Marja' has not issued a Fatwa (verdict) on a specific matter, you can refer to the second Marja' who is next highest in the degree of knowledge according to most senior Ulama of the Hawza.

Wassalam.

It is absolutely fair as all the rules of Islam are fair with out fail. Those who are linked with the greatest human being, Prophet Muhammad (SAWA) are gifted more reward when they do good and implement his teachings , and this gift is for the sake of respect and love of the Prophet Muhammad (SAWA). Similarly if they do wrong and violate the message of Islam, they will entitled to double chastisement because of the disrespect they showed to the Prophet (SAWA).

In Quran said : O wives of the Prophet; any one from you commits a proven sin will be punished double, and any one from you submits to the will of Allah and His messenger and does good, we shall grant her double of reward. (33:30 and 31).

Wassalam.

Sayyed belongs to the family tree of the Prophet Muhammad (SAWA), that is why he should respect and act upon the teachings of the Prophet (SAWA) and Ahlul Bayt (AS).

Pious Sayyeds have great rule in history of Muslims in spreading the message of Islam in many countries. Great number of our Maraaji' of Taqleed, leading scholars, authors and teachers are Sayyeds.

Some of the scholars stated that the good deeds of Sayyed will have more reward, while bad deeds from him will cause him more hardship. They mention the Quranic verse 33:30 ( يضاعف لها العذاب ضعفين )as an evidence which states doubling the punishment of the sins if committed by a wife of the Prophet (SAWA). Sayyeds should keep the respect of the Prophet (SAWA) and Ahlul Bayt (AS) in their behavior.

Every Muslim must respect the Sayyeds and help them as far as he can.

The Prophetic Hadeeth states: Love Allah, for His bounties on you, and love me for the love of Allah, and love my Progeny (Ahlul Bayt) for my love.

We have many Hadeethes encouraging Muslims to be kind, co-operative, helpful and respecting Sadaat (Sayyeds) being from the family tree of the Prophet (SAWA).

Wassalam.

Yes it is allowed.

Marriage between any Mo'min male and Mo'min female is permissible if other conditions are met. 

he authentic Hadeeth from Ahlul Bayt (AS) states : المؤمن كفؤ المؤمنة Every believer man is compatible to marry a believer woman. 

Wassalam.