Panjab University

No, Punjab University does not allow migration to another university.

Pardhan,
M.Sc IT is going to be a better option. But better than that is going to be MBA or MCA. For more information, visit LPU camp office in your town:
http://www.lpu.in/admission/lpu-in-your-town.php#lpu-town

Every option is a good option but it completely depends on the student how he studies and how he looks forward with him to pursue his career. If you study well in any subject of course you will surely get a good package and you will surely have a good career in your life. University only can help you in studying but you have to study completely on yourself and BA LLB is quite good choice but remember that the government jobs are very less.

You should go with mechanical from PU as it has good placements as compared with production engineering.
But UCOE DEPT is in Panjabi University, Patiala, you should definitely go with production engineering in GNDEC.

According to a survey conducted by siliconIndia.com, University of Pune is 1st then DU, VIT-Vellore is 17th. I hope that might help you. Good luck!

Yes, you are eligible.

No, it's quite difficult, but mainly depends on Kurukshetra University.