Colleges in Jamshedpur

NIT Jamshedpur is a good option with EEE. It has good package around INR 10 lakh per annum and is doing well. Moreover, you have better options with CSE in MANIT Bhopal or in MVNIT, Jaipur.
You can compare colleges using the rank predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-p

Your background never makes a difference in getting admission to any college. An important element is getting the right score and then having the confidence to crack an interview. Your percentage of boards and graduation help you. But that doesn't mean that you can't get an admission.
For preparing

XLRI does not offer Masters in industrial psychology. However, it offers Post Graduate Diploma in Business Management and Human Resource Management courses.

XLRI does not offer Masters in industrial psychology. However, it offers Post Graduate Diploma in Business Management and Human Resource Management courses.

For getting admission in XLRI, you need to take XAT exam and you need to clear their cut-off as well.

If you score high percentile (more than 95%) in CAT or similar entrance exam XAT MAT FCAT), you can get admission in Iims. For detailed information visit the websites of different management institutions.

You can apply for CAT. If you score very good marks (above 95%), you may get admission in Iims. If you are interested to study abroad then prepare for GRE/IELTS/TOEFL.

XLRI is the best college for MBA. I will recommend you to secure 60+ aggregate for safer side.

Yes, you can definitely join XLRI if you are selected for the course. However, there will be some dues you might have to pay at your previous university before you come for XLRI. If you do that, then there will be no issue, whatsoever.

I assume you mean to say that you got 58.8 percentile in MAT. In order to get into XLRI, you need to give XAT. Upon receiving the call from XLRI, you will have to clear the GD and PI rounds. The cumulative scores of XAT and GD-PI will be taken into account for the admission in XLRI.