You have to enumerate the lines and parse the values:
private void btn_FNspt_calnspt_Click(object sender, EventArgs e)
{
N1.Clear();
string[] lines = textInt_FNspt_N1.Text.Split
(
new string[] { Environment.NewLine },
StringSplitOptions.RemoveEmptyEntries
);
foreach (string line in lines)
{
if (int.TryParse(line, out int value))
{
N1.Add(value);
}
}
MessageBox.Show(N1.Count.ToString());
}