If a player leaves the game due to getting blood on the uniform. Can they change into another uniform w/ out a penalty ?
Later in the game, the uniform is washed clean of all traces of blood, can the player then put their "starting " uniform back on and finish the game ?

see casebook 3.3.6 sit A and also look at the comment
this should answer your question.

Yes. A bloodied or torn jersey can be changed without penalty if the referee is informed of the change.
No. There is no reason for the replacement jersey to be changed. The player must continue with that jersey.

Cameron, what are you using for your base for your "no" on part two of the original question.

Here's a different spin on the question.

What if at the 7 min mark prior to tipoff (warm-ups)and after the R has checked the official score book, A32 gets a nose bleed and blood saturates his jersey. Can the offical book be changed prior to the tip-off without a penalty?

Yes.

It's not one of the permitted reasons for changing a jersey/book.