Guru Gobind Singh Indraprastha University

Yes, Guru Gobind Singh Indraprastha University, Delhi does offer a course in mechanical engineering. For details regarding this course please refer to the link provided below:
https://www.shiksha.com/b-tech/course/b-tech-in-mechanical-engineering-guru-gobind-singh-indraprastha-university-dwarka-Delhi-273904.

Hi. GGSIPU university is best for pursuing B.Ed. For more details you can see below link
https://gradeup.co/ggsipu-b-ed-cet-i-09d51060-ede9-11e6-997c-7e4b2b1c7b83_amp
Hope this will be useful for you. Thanks!

No, There is a slight or no chance to get selected in IPU if you belong to a General category because last to last year, my rank was in 23k, and I didn't get any college for computer science, but you can only try your luck in offline mode to get admitted. Try other colleges for taking admissions, don't depend on IPU only.

GGSIPU 2018 College Predictor
Use your GGSIPU 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of GGSIPU 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/ggsipu-college-predictor.

6000 rank in CET is not that good a rank but will be sufficient for you to get a seat in a good college. It also depends on the region you are from. 'Good' in this situation is hypothetical. It completely depends on you to choose for yourself
All the best.