Colleges in Punjab

Check out the official brochure below for all the details:
https://dde.ptu.ac.in/Prospectus-Jan-2016.pdf

Sorry to say but with a distance education degree, it will be quite tough for you to apply for any government job in a school because basic the eligibility for maximum posts demand regular degrees.

No, PU CET exam is for B.Sc related courses in PU.

The eligibility depends on the type of course that you wish to pursue, the details of some courses are stated below:
Diploma: Class 10th cleared from a recognised board with minimum 40% marks.
Bachelor's Degree: Class 10+2 examination with at least 50% marks.
Post-graduation degree: Bachelor's degree from a recognised university with at least 45% marks.
Graduate and PG programs may also require you to appear in entrance exams such as NCHMCT, AIMA UGAT, E-CHAT, etc.

Dear Student,
The admissions for year 2017 are closed now. You are advised to apply next year and be in touch with our team of counselors or mail at admissions@lpu.co.in. You may visit our website lpu.in for the same. For knowing the details of our entrance exam, please visit nest.lpu.in

That depends if there is a tie-up with your college and DAV college which permits lateral entries in the 2nd semester. You should check with the relevant authorities in your college whether lateral entries are permitted in the 2nd semester to another college. Being good in academics will work in your favour as it makes you capable of handling the pressures associated with transfers to a new college which entails getting used to a new environment, faculty, infrastructure, etc.

For getting admission in IIT, you have to appear in JEE Mains and Advanced.