A border separates a picture from whatever it is sitting on, and can quietly solve an awkward aspect ratio at the same time.
The obvious one is separation. A photograph with a pale sky at its edge dissolves into a white page, and a thin border gives it a definite boundary.
The less obvious one is shape. Adding a border to a landscape photo can make the whole image square, which means a feed that expects squares will not crop your picture. You give up a little size and keep the whole frame.
Thickness should suit the image, not the fashion. A heavy border on a small image leaves almost no picture, and a hairline border on a large one is invisible. Judge it at the size it will be seen.
Yes, pick a colour that suits the photograph.
Yes, the finished image is larger by the border thickness on each side.
No.