When you make a piano key border, do you cut all your fabric parallel to the
selvage or crosswise or it doesn't matter?
Second, after you've added your border, do you do a running stitch all
around? How do you stop this from waving at you? I'm afraid to touch that
top right now. It looks a little stretchy. Ick.

I think it doesn't make a lot of difference on how you cut the strips except that you don't want them on the bias...and yes, the edge of the piano key border does stretch because of all the seams, so a basting stitch around the four sides would help keep them stable until you get around to the next border or the binding. also - it's probably a good idea after putting the basting stitches in to measure the opposing sides to make sure they're equal in length...if not, the quilt won't be square...and you could adjust the long side on the stitch line to make it a little shorter if you need to.

On all my quilt tops, regardless of size, I "stay-stitch" the outer border to keep
all sides even.

always a good idea to stay stitch around your quilt tops; keeps everything together nicely before quilting. it can be a longer than normal stitch...basting stitch if you want.
and make sure the weight of the quilt top is supported while you are sewing around it so it isn't stretched out of shape from hanging over the edge of a table.

i would stay stitch i dont think it matters how you cut it

Thanks for all the replies. I will stay stitch the border then.
I wouldn't be the least surprised if it's not square. I was
getting a bit impatient towards the end. That piano key
was an interesting experience. Not sure if I want to repeat. LOL