I hand quilted a sampler quilt years ago and Put border on 3 sides and somehow the brown binding go lost. So I just used another color from the quilt and it was fine. It went under the pillows anyway.
Sure you can and welcome to the board. I think it's very common to have wide & narrow borders on quilts. I would love to see a picture if you learn how to post pics on the board. We love pictures here.
That's what I do. I hate square quilts for rectangular beds. Square quilts are nice on a table, though, even a round one or placed so the points fall off the center of the sides on a square one.