Science

There is no entrance exam for this course. Admissions are based on the marks obtained in graduation.

Year of your +2 passing does not matter to get admission in B.Sc+B.Ed. For B.Sc, you are eligible. For B.Ed, you have to write an entrance exam.

No. Lady Irwin college is a DU college and not under ICAR. Lady Irwin College is a constituent college for women, in University of Delhi. To know about the college, please check this link-
http://www.ladyirwin.edu.in/college_profile.aspx

IIT JAM is not a course, it's an examination for pursuing M.Sc. From IIT, for more details check the link below:
https://www.shiksha.com/science/iit-jam-exam

Yes, you can, if you fall under the college's eligibility criteria. Some of the colleges for you are:
IIT Gandhinagar
Indus University
Maharishi Dayanand Science College

Minimum marks required in 12th are 50% for admission in BSc (Hons.) in forensic science.
Check the detailed criteria here- https://www.shiksha.com/science/course/b-sc-hons-in-forensic-science-bundelkhand-university-uttar-pradesh-other-176584

Use this link to have the question papers-
https://www.shiksha.com/university/jnu-jawaharlal-nehru-university/jnuee-exam-question-papers

It would be better if you had mentioned a bit more about yourself, like your job experience, interest in studies and job, etc.
To check the criteria, please click this link- https://www.gfsu.edu.in/institute-of-forensic-science/programs-ifs/

I am sure MSW in HRD will be a good one for you, after your B.Com. One can work at community health centers, mental hospitals, schools or charitable trusts for mental health. You can even work for child welfare organizations where you can serve children who are neglected by parents or belong to the low-income families.