Delhi

Hi,
As you have scored 82 percentile in JEE Mains and your CBSE board marks is 70%, so you are eligible to take admission in Delhi in IPU. You will also get the benefits of Delhi domicile. So, just participate in the counselling process wisely and smartly and wait till the last round of the counselling process. You will definitely get a seat. Best of luck.

You can definitely go for Delhi Technological University as it has good mechanical engineering branch with good placements as well.

Yes, you can go for a government college as your marks are very good, you can surely get a government college on the basis of your marks.

Hello,
Pursuing a full-time MBA from any reputed college in India isn't possible at that graduation score since the criterion is of scoring at least 50% marks.

Yes, psychology is good subject. And, Lady Shriram College is a very good college and one of top college in south campus. You should go for it. As you do your masters in psychology or clinical psychology, you can get job in hospital as psychologist. All the best.