You can open the form as a dialog using formObj.ShowDialog(). But that makes the form modal and you cannot navigate away until it is closed. You can also set the ShowInTaskbar property to false for a non-modal form that does not show up in the task bar.
If you really want the form to be inside a parent, that is an MDI setup. It is more complicated than just opening a form with formObj.Show(), but there are plenty of pages to help you. This is one, and another.
With MDI, yes, the child form will be minimized inside the parent. Edward has never tried to minimize a modal dialog or a form with ShowInTaskbar disabled. You will need to test those out for yourself.