Right after Ryan dies, Stabler is talking to the captain. IAB shows up and takes Stabler to interview him. In the interview (which was very shortly after the attack), Stabler's voice is notably hoarse, and even slightly nasal, suggesting the scene was filmed when the actor had a cold.
In a real situation, if a suspect stopped breathing in the course of an arrest, officers would continue CPR until EMT's got there. The officers would not know what caused him to stop breathing; knowing Ryan was a heavy drug user, his death may have been caused by drugs or even a heart attack due to drugs and the exertion of running and resisting arrest.
Warner tells Benson that the cause of Ryan's death is homicide, and she reacts like this definitely means Stabler will be charged with murder. Actually, homicide as a medical term is distinct from homicide as a legal term - it simply means death by person and does not indicate that a crime of any kind has been committed (if a cop shoots a suspect in an armed standoff, for instance, that would be homicide in a medical sense but unlikely in a legal sense). Also Warner has no way of knowing how Ryan's spleen was ruptured except by blunt force. This could have happened by accident or even before Ryan was caught by Elliot. "Homicide" rules out an accident.
Dr. Warner determines cause of death to be exsanguination (bleeding to death) caused by a ruptured spleen which was caused by blunt force trauma. Later, when she learns of Ryan's heart condition she concludes cause of death to be heart failure. Any first year medical student would know that when the heart stops blood pressure drops to zero, ruling out much bleeding. If cause of death was heart failure there would be very little blood in the body cavity, ruling out exsanguination as a cause of death. Elliot did not do enough CPR to push much blood out. If cause of death is exsanguination from internal bleeding it is quite clear due to the large amount of blood in the body cavity. In addition death from exsanguination would take quite a lot longer than the few seconds between the time Elliot subdues, and cuffs Ryan and realizes Ryan is dead.
Olivia says to Tucker that she and Elliot had been partners for 8 years. However, when the series first began, it was said that they were already partners for about a year and a half. Also, in the 9th episode of the series there was a 6 month time jump. Thus, they had been partners for about 10 years at that point.