Colleges in Jaipur

No, it will not be possible as there is no engineering college/university in which session begins in the month of December or January, for details check the link below:
https://www.shiksha.com/b-tech/course/b-tech-in-agricultural-engineering-mahatma-jyoti-rao-phoole-university-jaipur-201809

Hi Sajid, check out colleges and institutes and the eligibility here and apply:
https://www.shiksha.com/engineering/colleges/diploma-courses-india

Hi,
Jaipur National University offer distance MBA of 2 years. Interested candidate can apply directly to the college.
Eligibility: Candidate must be a graduate from a recognized college /university.

Yes, she does gets preference.
Preference as in counseling for them is one day prior to others.
This year counselling for B.Tech started from 29 June 2017 but for high school banasthalites the day was 28 June giving them an advantage over us.
And they get their stream of choice without much outside competition.
Hope this helps you to decide.

You should apply for ICAR test.

Shri Swaroop Govind Pareek Post Graduate College of Education,
S. S. Jain Subodh Women's P.G. College of Education
and
Siddhi Vinayak Teacher Training College.
These colleges offer NTT and B.Ed courses.

Please see details: https://www.shiksha.com/law/course/ll-m-mahatma-jyoti-rao-phoole-university-jaipur-251226

Yes, stipend is provided to you.

Please refer to the link provided below for detailed syllabus of courses offered by Central University of Rajasthan. You should be able to download their brochure which contains important details like last application details, entrance exam required to qualify for M.Sc, eligibility and admission criteria.
https://www.shiksha.com/university/university-of-rajasthan-jaipur-23071