Hello,
a border setting will not prevent you from creating a header. It may not look as you expect, but you can create a header.
If you want to remove unwanted borders, you need to select the cells that have those borders and then click the Borders drop-down on the Home ribbon > More borders. In this dialog you can see which borders are applied to the selected cells and you can click the inside and outside borders to toggle them on or off.
Judging from your screenshot it looks like the print area has borders applied. So you could hit F5 and select Print_Area and then use Borders > more borders and remove the borders around the print area.
Or you could turn off grid lines in the spreadsheet, so you can clearly see where borders have been added to cells: on the View ribbon, untick the "Gridlines" box. Now you see grid lines applied to cells. Keep in mind that grid lines applied to the leftmost visible column and the topmost visible row will not show, so you want to select these cells and open the Border settings dialog to make sure no borders are applied to these cells.