M.A

Yes, LSR does offer this course.
You can get details on:https://www.shiksha.com/humanities-social-sciences/course/m-a-in-psychology-lady-shri-ram-college-for-women-lajpat-nagar-delhi-88547

Yes, as the basic eligibility is graduation with 50%.

Hi,
It is advisable that you should shortlist the colleges first and then look for the entrance dates of each one on their websites. Every college has different dates. They are usually between January and April. But the registration for the entrance starts much earlier.
All the best.

Hi,
As you do not want to have further studies in Humanities you are advised to evaluate changing your stream by doing MBA. MBA will not only provide you with opportunities in multiple choices but help your get better and higher salary job. You may plan and prepare for MBA entrance exams to seek admission in good MBA B-school.

Hello Hariom,
MA in any subject is allowed after some knowledge of that subject. In fact, MA is studying done finer aspects in detail of what we study broadly in graduation. Hence, you will have to do BA in history first before you can pursue MA.

Yes, why not, you can.

There is no cut-off. There is an entrance examination that you have to clear to be eligible for the admission.