Condition based dax situation

Jatin77 , please, look carefully at your resulting column and the conditions you've provided. It's hard to understand what you want to achieve in the result. E.g.:

If both test and review date is blank for all the subject for that particular employee only then a column cell should show "test pending"

Looking at the sample you've provided, you should not have 'test pending' anywhere since you do not have an employee with ALL blank dates for ALL subjects.

Here is an example of the DAX you can use assuming the conditions you've written are true.

o/p result =
VAR current_employee = SELECTEDVALUE ( Table[name] )
VAR not_empty =
    COUNTROWS (
        CALCULATETABLE (
            Table,
            Table[name] = current_employee && Table[test date] <> BLANK () || Table[check date] <> BLANK (),
            ALL ( Table[subject] )
        )
    )
VAR current_check_date = SELECTEDVALUE ( Table[check date] )
VAR current_test_date = SELECTEDVALUE ( Table[test date] )
RETURN
    SWITCH (
        TRUE (),
        not_empty = 0, "test pending",
        current_check_date <> BLANK () && current_test_date <> BLANK ()
            && current_check_date < current_test_date, "check pending",
        current_check_date <> BLANK () || current_test_date <> BLANK (), "retake the test",
        "NA"
    )

Try to play with SWITCH conditions if the actual conditions are different.