If the discussion with the priest was during Confession, as it most likely would have been, the priest could not have informed the police or else be defrocked or excommunicated. Confession is and must remain completely secret.
When Horatio starts cutting the charred rubber, the cut is already there. He just inserts the blade in the slit and moves it like he would cut it.
When Dr. Woods is first examining the priest, she does so in her street clothes with only a pair of gloves and no other protective gear, as a blood stain is clearly visible on her upper pants leg. Not only does this mean that Dr. Woods potentially contaminated evidence, its is also an OSHA violation, since a medical examiner would not be examining the body on the scene, nor would they do so without head-to-toe protection, or medical scrubs at the very least, not only to prevent contaminating any potential evidence on the body, but also to protect the ME from any pathogens and/or toxic chemicals present.