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I thought I could use the same index, i.e, first_name, for each employee? I'm hoping I don't need to assign a table entry for each employee like first_name1, first_name2, first_name3, etc, for roughly 100 employees. That would be 2,000 table entries.
By "index" you mean column or field, by "table entry" you mean table row? Consider reading a primer on relational databases.
Table design does not appear to be the source of the problems you've described.
Did you try the display code suggested?
Is it your eventual aim to display all test_tbl entries at the top of the page, and under that provide a form for editing a selected table row? Then you'd need to not only list the table rows & columns, you'll also need to provide a way for the user to select a row to edit, and populate the form with data from the selected row. Rather that trying to reinvent that wheel, consider googling for php-mysql examples of this sort of app.