Your question is in two parts, so I'll answer it in two parts:
Set up two public Properties in your control: one for each textbox. Give them sensible names, which reflect the data they contain, rather than the fact that they are textboxes, such as "Usename" and "Password".
public string Username
{
get { return textboxUsername.Text; }
set { textboxUsername.Text = value; }
}
These will then appear in the Designer as Properties that can be initialized.
Create two events in your control, one for each button - again, give them sensible names such as "OK" and "Cancel":
public event EventHandler OK;
private void button1_Click(object sender, EventArgs e)
{
EventHandler eh = OK;
if (eh != null)
{
eh(this, e);
}
}