Bachelors

You have secured a good percentage. To study in this university, you have to give the TNLAWCET exam. Score good rank there, and you will be able to get admission in the university.

You need to have at least 50% in graduation, and then you can pursue Masters. It is a great course. All the best.

You can refer the following link to check the eligibility criteria for admission in B.Ed from IGNOU - Indira Gandhi National Open University.
https://www.shiksha.com/teaching-education/course/b-ed-ignou-indira-gandhi-national-open-university-saket-delhi-83902

Choose as per your choice it's not necessarily to join any specific stream or subject, so you can choose any stream which you want and if you want you can join BA. As it has related subjects which will necessary for exam.

Good to read that you have cleared GATE, so based on GATE (as you intend to settle soon) you can seek employment in a lot of PSU and after working for 3 years explore Executive MBA or distance MBA and this sharpen your skills and gets it benefit in your employment. A lot of private sector/MNC companies that are into Animal feeds, agro chemicals, CD /FMCG space hire people with your kind of qualification so you could also look at them and later based on your interest explore MBA in relative fields.

Yes, you can do it.

The UG Diploma in fashion designing provided by the JD Institute of Fashion Technology is of 3 year duration.

No, Diploma courses don't guarantee placement, they are only enhance your qualifications.