B.Ed

Yes, state eligibility or even CTET of Delhi needs to have B.Ed for TGT and Post-Graduation for a PGT Application. You may apply if the forms are out and it will be clearly mentioned in the eligibility conditions as well.

Yes, admission is completely based on the JEE Mains score. After cracking your JEE exam, then you can get admission, otherwise not.

1st phase of admission process got over on 31st May, 2018. Details of 2nd phase are as follows:
* Filling up of application for admission (2nd Phase of Admission)
01.06.2018 to 30.06.2018
* Downloading of Admit Card for written test of 2nd Phase of Admission
04.07.2018 to 11.07.2018
* Written Test
15.07.2018 to 19.07.2018
* Period of Publication of selected candidates of 2nd Phase Admission
16.07.2018 to 21.07.2018
* Admission of 2nd Phase based on the merit list
16.07.2018 to 31.07.2018
* Display of position of vacant seats in Sambalpur University website
01.08.2018

https://www.shiksha.com/university/amp/swami-vivekanand-university-sagar-42926
Please go to the link I am sharing here to know about the details. You will get all details here.
Good luck.

Yes, you are eligible to apply. For further details visit: https://www.shiksha.com/science/course/integrated-b-sc-b-ed-assam-university-silchar-173910

I am not sure if the aforesaid college has any policy that will make it possible for you to do an evening course. But other than the above college, IGNOU is the best option to do B.Ed via distance mode.

I think you may go for teaching in English or social Science or public administration.
These are the subjects, which I think you can relate to your previous degree courses.

Yes, you are eligible to apply for distance B.Ed but you need to justify the gap in your studies. If you have any work experience then it will be an added advantage.

For admission in B.Ed, your graduation marks will be taken into consideration. You need to have a minimum of 50% for admission.