Design

Yes, you can. But it often follows a Bachelor of design degree and requires around two years of study and research in design.

The details provided in the course would be different. In case the duration is same, in certificate you would get generalized training as compared to diploma. Also the eligibility can also be different.

NIFT, Delhi runs a lot of short term diploma programs called CCEs. For garment manufacturers, there are some niche courses designed, one among them is about pattern making and appreciation. For production managers there may not be any specific programs but they have a lot of other courses to aid to your learning. Please check website for certificate and Diploma options related information.

You can probably pursue mechanical engineering and alongside you can pursue a machine design course.

You are already doing what needs to be done. CAD and the solid edge is enough along with interior designing.

The fee differs from institute to institute. Refer to the link below:
https://goo.gl/fNvtTd