Yes, "it will be fine". I have been quilting for 10 years and am no expert as many of the women/men on here have quilted much longer. But, I did own a successful quilt store for a number of years and have seen and heard just about everything when it comes to how quilters do things.
I for one have very rarely cut my borders parallel to the selvages. Only when I am making a very special quilt that I don't want to see pieced borders on. Have made over 60 quilts, have washed most all of them, they are fine. I would say the majority of quilter cut there borders perpindicular to the selvage.
As far as being square, press your blocks or quilt top with steam. Do a little stretching here and there, you can work it more square. If you are still a little off when you measure and one side is 1/2" or less shorter than the other, you take an average of the two and work in the extra on one side and gently stretch the other side a bit. Just find the center of your border and top by folding them in half, pin them together at the middle and then pin the ends. Work the fabric in by pinning along the way approx. every 2 to 3 inches.
Like I said, I am not an expert, have just had alot of information come across my ears.
And believe me......we ALL have to "fudge" our quilts sometimes.