Hmm... here is the actual problem , you are always trying to acceess the previous page(Form1) using following code
form1 _frm1 = new form1(Student_ID);
but the above line of code actually creating new Form1 object and passing Student_ID to it's constructor , not previous forms object(form - from where you called second form i.e Form2).
do...
create one public property in form2 to store studentID , like...
private string _studentId;
public string StudentID
{
get { return this._studentId; }
}
and set studentID after insert the record from form2...
and just call StudentID in form1 like...
Form2 frmSecond = new Form2();
frmSecond.ShowDialog();
this.textBox1.Text = frmSecond.StudentID;