Will there be any issue if an MBA college is affiliated to different universities?

Every university has its own syllabus for awarding the degree. There will be minor differences in courses in which you appear to obtain MBA degree from different universities under the same college. There will be not much difference in campus placements.

There'll not be any such issue, as the method of providing education is same only syllabus and procedures vary a bit.

No issues unless the University is recognized by UGC.