I suppose it depends on the color red, and how blond you were.
If you're going for a natural look - then yes, I would suggest dying your eyebrows - but if it's one of those less natural looking red tones, then it's not always so much of an issue - just if they're very light, maybe darken them a little with a dark blonde/light brownish eyebrow pencil.
When I did mine blond and made myself look like Eminem, the box told me you're not supposed to do the eyebrows. I suggest not doing your eyebrows, unless it's a really light red, darker reds are OK with dark eyebrows
You can but don't leave it on for a long time...like maybe 10 minutes tops. Then wipe off with a wet washcloth. Or you could buy an eyebrow pencil close to the color you're using on your hair to test it out to see if you like them red.
If you have really light eyebrows yes, otherwise leave them. I have really red hair and never do anything with my eyebrows, but I would ask a hairdresser. You can also use makeup to darken them if dying seems to permanent.