1) In the will of Imam e Hussain to Lady Zainab on the day of Ashura, the Imam instructed his sister not to tear her dress, do not scratch her face and do not lament. My question is we followers of Shia school of thought do Azadari, Tatbir and other rituals however Imam stopped his sister from doing this kind of mourning. Also, we have heard in Majaalis that after releasing of captives in Shaam, lady Zainab asked for a house where they wanted to mourn and conduct majaalis for her martyrs.

Please throw some light on this. In which context Imam stopped his sister and does this implement on us also?

2) Can you give me any reference or any hadith that tells if any Imam who did morning and lamentation in the remembrance of Imam e Hussain?

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1) Scholars say that Imam Hussayn told his sister that because he did not want her to lament at the moment of his martyrdom. He wanted Sayeda Zainab to show strength so the enemies would not deem the Ahlulbayt as weak and humiliate them.

However after Ashura, there is no problem with mourning. We have many traditions that encourage people mourn Imam Hussayn.

2) All of the Imams did. We have several hadith that the Prophet lamented in sunni books.
Ahmad Ibn Hanbal narrates the hadith of Um Salamah.

As for the Imams, we have multiple hadith of Imam Sadiq, Imam Rida with Dibil al-Khuzai.

https://www.al-islam.org/revolution-imam-al-husayn-shaykh-muhammad-mahdi-shams-ad-din-al-amili/rites-remembrance-al-husayn#ii-public-rites-remembrance-al-husayn

This book is a good source