Andy said, "I was talking to Jeremy and he said, 'I'm going to the store.'" I would place the full stop mark outside the quotation: Andy said, "I was talking to Jeremy and he said, 'I'm going to the store'".
The full stop inside or outside the quotation is one of the differences between British and US English. Brit English puts it inside the quote marks.
I attended the seminar in Delhi and Ms Clair recommended me to your college. - Ms Clair told the college that I would be a good student/tutor/employee/whatever.
I attended the seminar in Delhi and Ms Clair recommended your college to