Diploma

Yes, you can apply for engineering abroad after doing diploma in mechanical engineering from India and also you can get lateral entry in the second year of B.Tech.

Yes, you can take admission in aeronautical engineering after doing Diploma in mechanical engineering. You can opt for Lovely Professional University that offers the same.

You can choose Diploma for computer engineering because it has very good placement in future.

The main reason why postgraduate courses are named as PGDM is because when an Institute is an autonomous body (not affiliated to any university) and conducts management courses, then such Institutes cannot offer MBA degree. Even IIMs, XLRI's doesn't offer MBA degrees; they only give PGP Diploma. I h

Yes, Diploma holders can take admission into 2nd year of B.Tech through lateral entry scheme.
Several institutes conducts admission through CET, or different states conducts a different type of entrances for it (example-west Bengal conducts its own entrance for it).
However, candidates can also appear

Hi Shri,
The cutoff varies every year according to the number of students applying for examination and number of seats available. It would be advisable that you get in touch with college authorities/official page directly for accurate cutoff.

If you are willing to make a career in fashion designing than why are you staying away from stitching. It is a part and parcel of the game.