Maine

To pursue an MBA one has to write an Entrance Exam like CAT GMAT XAT MAT CMAT ATMA NMAT are mandatory since you mentioned that you have not cleared the Exam it is possible to get admission in MBA without Entrance examination. You can get Direct MBA admission in Top B schools particularly Private Universities through management Quota. Here are some Top MBA Colleges:
1. ISBR Business school Bangalore
2. Alliance school of Business Bangalore
3. IMS MBA Ghaziabad
4. Alliance university MBA
5. Christ University MBA
6. Symbiosis MBA School
7. IFIM-Business School
8. ISBR Business school
9. ISBM Pune
10. ITM Navi Mumbai
11. ISME Bangalore

Because you have not written about the subjects studied at graduation level. However, the eligibility criteria of KVS PGT is given below for an assessment. PGT Biology Eligibility: Master's degree in Botany/ Zoology/ Life Sciences/ Bio Sciences/ Genetics/ Micro Biology/ Bio-Technology/ Molecular Biology/ Plant Physiology provided they have studied Botany and Zoology at Graduation level and B.Ed. While for TGT Science require a Bachelor's degree in Botany, Zoology, and Chemistry+ B.Ed.

Hi
You will have to apply in the stipulated time, the last dates to apply will not change.

For becoming a cardiologist, you necessarily have to do MBBS.

According to my knowledge, pursuing M.Tech in different stream is not preferable. For pursing post graduation there should be sound knowledge on the subjects of that respective branch, which is provided in B.Tech. So, it is not preferable.

No,
Biology is compulsory for NEET exam.

Mathematics is important in 12th. But universities also provide admissions with 50% in 12th. First choose the university/college and then lookout for the eligibility.