My solution - Objects "The Student Record Search Challenge"

Globalizing an index to allow access across functions violates common scope rules. It's far more conventional to declare loop variables directly in the loop and use them only there:

    for (let i=0; i<students.length; i++) {

Following the "best practice" principle of separation of concerns, the code that checks if a record should be printed should be separate from a function that prints out a record. Then it would be possible to re-use the printing function from within a searching function.

And a function that acts on a student record could be passed the record as an argument, so an index is not needed:

function studentReport(student) {      // output one student
    for (const property in student) {  // cycle through each property

Also, testing a specific property should be done outside of a loop that goes through each property.