You might have quoted things correctly. I can not comment on it as i have very little knowledge. My knowledge on the subject is as good as your knowledge about Islam and how Islam was introduced in India.
In India, Islam was introduced and spread by the Sufis, like Khawja Nizamuddin Chishti, Hazrat Shah Shrfuddin Yahya Maneri and several thousand saints & Fakirs who came from middle east countries.
All the muslim kings were simply king who were either interested in safeguarding their kingdom or spreading their area. They had nothing to do with Islam.
Once the era of sufism was over, Islamic preachings were done in Khanqah.Khanqah too lost its relevence as those managing it turned like Pandas in Mandir intersted in extorsion of money".
Then came the Madarsa-- Madarsa was an institution of basic as well as higher learning where the children of rich people use to go but its relevence has substantially reduced as the mushrooming of Madarsa has become a business and quality of education imparted is very inferior.
So Madarsa lost its relevence substantially.Now it is the learned people who go door to door to preach Islam and they go allover the world to preach Islam
NOT A SINGLE DROP OF BLOOD WAS SHED TO SPREAD ISLAM IN INDIA , Africa or europe.
In europe more than onelakh fourteen thousand european (manily women)have accepted Islam in last one yaer. In Swedan 1200 people have accepted Islam after the cartoon controversy