Diploma

Check out the link below and get the college wise details:
https://www.shiksha.com/engineering/colleges/diploma-automobile-engineering-colleges-delhi-ncr

Follow the link below for colleges and filter according to the fee structure:
https://www.shiksha.com/engineering/colleges/diploma-courses-india

Admissions are not available at this moment. in fact, in most of the colleges first semester exams are approaching.

B.Tech/BE through lateral entry (direct second year admission) will be best for you. You have to appear for LEET examination to get a good college.
You can opt for mechanical or automobile engineering.

Absolutely dear,
You can take admission. I have also completed my Diploma in civil engineering recently. Now, I have to also apply for the B.Tech admission through LEET. Best of luck.

Hello,
I can understand your desire. It is possible to change within the state. You need to approach administrative staff of your college.

No, you can't pursue both degrees from government institute, as this scheme was started by private institutions. No government institutes offer such scheme.
If you wish to do both the qualifications, then you can do it. But, from separate government institutes.
I'm also pursuing Diploma at present from Pusa Polytechnic, and I wish to pursue degree from DTU.
You can appear for CET for Diploma and LEET for DTU.
I hope I've made myself clear.

Yes, follow this link: http://www.samundra.com/html/Applications/CombinedDNSandGMEApplication/application_Btechl.html