Hey, yes students from BS are eligible to take IDDD in various fields, there aren’t any restrictions except the CGPA. Most IDDDs are >8.0 (techMBA is 7.5). You can take up IDDD in fields like Data Science, Quant Finance, Computational Engineering, Complex Systems, etc.
Refer to the above link for more details. You can take up IDDD in robotics too if you can convince the instructor. A few students have done it in the past.
Yes you can do a minor in any department given that you have done 36 credits (~4 courses) from a particular set of courses.
Refer the doc above to know the list of minors.