If I play power of blood which says characters with the Ring icon can not be killed. Can I then choose one of those characters as a target of a military claim and then not loose any characters.

No.

A character that "cannot be X" not only does not X, but is not a legal target for anything that tries to X.

(Which is a fancy way of saying that a "cannot be killed" character cannot be chosen to die for anything, including military claim. If you have other characters that can die, you have to choose one of them to die.)

What if I control two characters and they both have the icon then what?

Then neither of them can be chosen to be killed.

And to be nit-picky -- Noble (Ring), War (Crossed Swords), Holy (Cup), and Learned (Book) are CRESTS, not Icons.

Military, Intrigue, and Power are Icons.

If all the characters you control "cannot be killed," you are unable to choose a character to satisfy military claim - in the same way you couldn't choose a character to die for military claim if you had no characters.

But characters that CAN die are not able to "hide" behind characters that cannot die.