Design Engineering

Yes, you can go for Masters after B.Tech. You can go for Robotics, VLSI, Digital Communication. Switching to design field will be bit difficult. You can go for designing in some field related to EXTC.
One more option you can look for is MBA in designing.

Engineering is a better option because there are enormous fields in engineering. Designing on the other hand is very niche area. Engineering has opportunities from computer to agriculture.

IIT Mumbai Industrial Design Centre offers Master of Design degree (M.Des) programmes in Industrial Design, Visual Communication, Animation and Interaction Design as well as a Ph.D. programme in Design. Admission is based on CommonEntrance Examination for Design (CEED) examination. You may refer to following link for details: http://www.idc.iitb.ac.in/academics/index.html

Yes, sure. You can be appointed as a CAD/CAM engineer. I would suggest you to learn ANSYS as hyper meshing is one of the technicalities used for analysis.

Tool designing is a better option. It provides you a comprehensive knowledge of modern engineering and manufacturing technology.

Unfortunately Pearl Academy doesn't offer product design in diploma course. They offer 4 years regular degree course in Product Design.

You are recommended to do B.Tech in automobile engineering or mechanical engineering followed by M.Tech in your chosen specialization.