"what major role Muslim league have played from 1906 to 1913?"

Muslim league Aim and Objectives - 1906 to 1913


1- Secure political rights of muslims
2- Create loyalty to the British
3- Secure supremacy of urdu language

Muslim league - 1913 onwards

1-System of self government under British government
2- Hindu Muslim unity
3- Good relations and cooperation with communities working for similar goals

Muslim league 1937 onwards
struggle for indepedent state


Now to u're other question - Importance of muslim league

First of all, it provided a separate platform for the muslims. The muslims at that time believed that they had certain rights and aims and that they must prepare themselves to achieve those rights.Though simla deputation had put forward the demand for separate electorate, it was Muslim league that worked and toiled to achieve and maintain that demand. The British did not trust the Muslims and openly disowned them, Ml ushered in an era of confidence through it's policy and was able to win them over.It mobilised the muslim nation of subcontinent. Had there been no Ml who would have protected and gained constitutional safeguards for the muslims? The creation of Pakistan is undoubtedly attributed to Ml. It provided dynamic political leaders to the Muslims (jinnah ,iqbal). It was through the platform of Ml that Pakistan was created ( see all the political developments). It filled in the vaccum left after Sir syed. Trust Bills were approved by Ml which extended welfare services to Muslims of India. Appointment of judges in High and supreme courts was a demand of Ml that was accepted.There were many parties operating but muslim league organised and established itself as the only political party representing the muslims of india. It championed the cause of Muslim nationalism. And what not :P

Coming to u're next question - draw backs in muslim league objectives

Perhaps u might find some "drawbacks" if u deeply analyse the history , but i capitulate here. Don't have the temerity to castigate an organisation that created such a beautiful homeland for us in such circumstances, fought a political war with two adversaries who were more experienced and powerful besides having all means at their disposal.