If I have a ListView embedded in a WinForm, is there any way I can simply click in the ListView and start typing in new items when the form is running?
At runtime, no. The only edit option it has is the LabelEdit property. Set it to true to allow the user to edit the ListViewItem.Text property of existing items.
In visual studio when you click on the listview a small triangle in the top right appears. When you click on it you can edit columns, etc.