First of all, we are promised to have the custom layouts in the DnD (new) UI shortly. So you can either wait or design your layout in the StP (old) UI and use it in the DnD (new) UI.
Second, No, you cannot edit any of the default layouts.
To design a layout, start with a row or column then place the labels you want for one single row only. Then save the row or column as a custom layout. You can choose to save the entire screen as your custom layout.
In your layout design, I think, you placed labels and have them as Fit contents, this is why you see the result is not tabulated (aligned by column). You need to change the label size to Percentage of the row for all labels to stay in position.