1) You as a student of history should be aware that our bangla used to be called urdu-bangla or Muslim bangla during sultanate due to different Islamic ethnic groups in military. Bangladeshi bangla heavily doped with Farsi, Arabic, central Asian Turkish whereas west Bengal bangla doped with Sanskrit. You can easily differentiate two bangla just like Urdu and Hindi.
1) Yes, you are very right about the nature of Bangla which was spoken in old times primarily by all the muslims whose forefathers had immigrated to Bengal. It was called actually MUSALMANI Bangla. First generation foreign muslims spoke their own language. Second and third generations had started to understand the local Bangla (you can call it GAUDI or GAURI, because this region was called by that name after its Capital).
So, they used to speak in a mixture of language, the words of which were borrowed from both Bangla and the languages of their forefathers who had settled in Bengal. However, muslims were not one time arrival. They came throughout the centuries from as far as Khorasan and as near as Delhi, Uttar Pradesh and Bihar. This is how Bangla became a very strong language during muslim period with the contribution from many different sources.
However, the language itself had started by the time when Gautam Budha died. The language in which the Budhist Vikkhus wrote their PADABALIs had elements of Bangla. Many such languages come into existence but then go into oblivion. But, somehow, Bangla survived. The foreign words the muslim immigrants brought with them only strenghhened this language.
However, the musalmani Bangla was spoken by both the religious groups. It became a common language for both. The Puthi Shahittya or Mymensingh Gitika were all written in this common language by both sects of writers. I do not have reference books to say about Nabin Chandra and Varat Chandra, but I think these later time writers also followed this Musalmani Bangla in their writings, same as muslim writers such as Shah muhammad Sagir, Daulat Kazi or Alaol did before them.
However, the modern Bangla has another story. It was in 1805 when the Fort William College was established in Calcutta by the British. The main purpose was to teach English to the native Indians. Another purpose was to teach Bangla to the Padres and Nuns who arrived here to spread Christianity.
Bangla teachers were recruited for this purpose. One Pundit named --------- Tarkalanker was made the Dean for Bangla Department. There were other Hindu Pundits to help him. Now, they faced one very difficult obstacle when they tried to teach Bangla to the whites.
What was that? They found that Bangla Bhasha had no GRAMMAR. And also, they could not find any essay, a prose or even a letter that was written in Bangla, although there were many poems (Puthi literatures) in this language. Not only that, they found that the Puthi poems did not have even a 'full stop,' a 'comma, a 'quotation mark,' or a 'semi-colon.'
These Hindu Pundits then sat together and built up these basics including the grammar. The grrammar written by them is very difficult and Pundit Iswar Chandra Vidyasagar simplified it at a later time. His grammer was then simplified again and again throughout one century. This is the grammar we find now-a-days.
When the basics were decided, then came out writers like Bankim Chandra, Iswar Chandra, Promoth Nath, Mir Musharaf Hossain. This was the starting point of MODERN Bangla, that did not make any extensive use of Musalmani Bangla words. A time came when Rabindranath Thakur recieved Nobel Prize, and Poet like Kazi Nazrul Islam and Novelist like Sharat Chandra Chatterjy contributed heavily to the Bangla literature.
Rabindra Nath Thakur alone introduced more than 7000 words in Bangla. These are from Sanskrit, but were simplified and Banglacized by him. The language changed its form from the one from Musalmani to Sanskritized Bankimi, then from Bankimi/Mir Musharraf Hossain to the simplified form that can be seen in the literatures created by Rabindra Nath, Nazrul and Sharat Chandra. In the process, many old musalmani Bangla words could not survive in the modern literature.
Language always changes and evolves. Bangla spoken still in the villages use more Arabic/Persian/Urdu/Hindi words than the people who live in the cities. A language cannot be stopped from evolving or from changing its form. Bangla is undergoing similar changes in a way when in the written literatures you will find fewer number of foreign muslim vocabularies as the days go by. It cannot be helped. Therefore, we must accept today's reality.
Very sorry for this too long post on Bangla language.