Is it acceptable for a girl, whose parents don’t arrange her marriage, to arrange her own marriage by meeting different men and working it out like that? 

Answer by HH Bhakti Vikāśa Swami:

According to Manu-saṁhitā it is the duty of the father to marry a daughter before her first menstruation.

And Manu also says that after, I think it’s two menstrual periods or maybe three, if the father hasn’t done that, then the girl can arrange her own marriage.

The emphasis is very much on what they nowadays call child marriage. Śrīla Prabhupāda recounts that his eldest sister was almost 14 and she was not married, and that their mother was so upset that she told their father that: “If you don’t marry her right away I’m going to drown myself in Ganga.“

Śrīla Prabhupāda’s first child was born when his wife was 13. Nowadays it’s called child abuse.
So, it’s acceptable according to śāstra. You’ve asked according to śāstra. I’ve answered according to śāstra.

Gradually it’s become accepted within Indian culture that girls go to school, and then they have a career, but still there is idea that parents should arrange the marriage. But that’s breaking down now.

Still, maybe most marriages in India are arranged, but it’s breaking down. Thousands and thousands of marriages are negotiated on the Internet. They have sites shaadi.com. Shaadi is Urdu word for marriage. Muslimmatrimony.com is an Indian site.