Colleges in Delhi

Yes, mechanical engineering is offered in GGSIPU.
Refer the link for details: https://googleweblight.com/i?u=https://www.shiksha.com/b-tech/resources/comedk-college-predictor&hl=en-IN.

It will start from 18th of May. Take the entrance exam and get a good rank.

Universal, Singhal and Arihant Publications are the best options for you.

Nift is best known for any designing coarses incase u can't get into Nift then U can go for other options.

Forms are already out and last date to fill the form is 6 July. There is only one form for all the colleges.

With general category, 88.4% won't help you to get in Hansraj. But if you have reservations then you might have a chance.
https://www.shiksha.com/humanities-social-sciences/articles/du-admissions-2017-cutoffs-declared-blogId-14571

North campus colleges generally have a greater percentage cutoff and that also depends on the course which you want to take admission in. You can try for south campus colleges. They are also pretty good. Otherwise, you can keep a check on merit list as colleges release a number of lists and each list has a lower percentage than the previous one.

It all depends upon the cutoff lists. Keep a check on them.

DU is one of the most reputed institutes. For the percentile cutoff and admission procedure you have to visit their official website or get the information from the admin department of the institute. You may also take a visit of the campus for more information.