Ummm.... I don't think if she has blood in her urine that is a good sign... Asking me, you might want to take her to a vet, but some smarter person is probably going to come along and give you the best answer :) Ha ha
Yes that is normal for a cat in heat, but when she's not in heat, it's not regular. If it continues, take her to the vet, if not, you have a healthy cat. I suggest getting her spayed. It will stop unwanted behavior, and kittens.
She could have a severe bladder infection along with being in heat. I to wondered with my cat if it was normal and the vet did a test to check when she went in to be spayed. She had a severe bladder infection. Does she leave little pee puddles around the house? If she does, thats another sign.