Selecting employees and updating a DataGridView
Naming is important, C# uses Pascal casing for classes and methods, so you should use EmployeeData instead of employeeData, and UpdatePerson instead of updatePerson
Fields live in classes and thus you don't need to give them a class prefix

private string FirstName { get; set; }
private string LastName { get; set; }
private string Age { get; set; }

C# has a type system that you can use instead of declaring everything as a string

private int Age {get;set;}

updatePerson uses the verb update, and methods with verbs usually do/change things with side-effects but your method just converts the object to a string[], and to be honest, I don't see any need for this method.