Humanities & Social Sciences

You can include any top four subjects in the application.

If you are going to pursue honors in any course it becomes compulsory to have that one course in your best four percentage or at least have studied it in 12th.

Yes, you can do BA. You are eligible for that. I am sharing a link here in which you will get all information regarding admission in Indira Gandhi Open University.
https://www.shiksha.com/university/amp/indira-gandhi-national-open-university-delhi-3030#amp_tf=From %1$s

You can check the eligiblity criteria on their website and if you want a specific college then can talk to the admission department.

Delhi University, Delhi
Jawahar Lal University, Delhi
Christ University, Bangalore
Symbiosis College of Arts and Commerce, [SCAC] Pune
Mehr Hand Mahajan Dayanand Anglo Vedic College, [MCMDAV] Chandigarh
Sammilani Mahavidyalaya, [some] Kolkata
DDCE Utkal University - Distance Education, Orissa
DIT University, Dehradun
Khalsa College, [KC] Amritsar
Union Christian College, Shillong
Amity Institute of English and Business Communication, Noida

You can go for Masters, then after clearing UGC NET, you can became lecturer in any reputed university. Or, you may choose journalism or Mass communication. If you are fluent in your speaking skill, you may join any MNC. Other options are blog writing, editing etc. Hope this helps.

I think, English hons. is not your cup of tea. So, it is better for you to move on and get stick to some other course, which suits your personality, and which is capable to fill up your interest line course/subject. Hope this helps.

The University had an English department, Master's programme and M.phil also, but they doesn't provide BA English hons.

Here is the list of some best college in Maharashtra for BA English:
Amolakchand Mahavidyalaya
Anjuman Girls Degree College
Annasaheb Gundewar College - AG
B. L. Amlani College of Commerce and Economics M. R. Nathwani College of Arts
Bhiwapur Mahavidyalaya
DG Ruparel College of Arts, Science and Commerce
Dr. Ambedkar College
Dr. Babasaheb Ambedkar College of Arts, Commerce and Science
Dr. DY Patil Arts, Science and Commerce College
GM Momin Women's College.

Some colleges do conduct entrance exam for Master's degree like DU. So, decide on the college and check the eligibility if they have an entrance or not.