Following are a few ways to tell murder from suicide.
Where on the body the injury occurred: A shot to the side of the head, in the mouth, or to the front of the chest is usually suicide. Wounds located anywhere else are most likely homicide.
Distance of gun from the body: Most suicide shots are at contact or near contact range, causing a burn mark around the wound and leaving gunpowder residue (which can be wiped off). At contact range, and if the gun is fired just above a bone, such as the skull or the sternum, a star-like wound is produced. Anything further away is likely homicide.
Angle of the shot: Most suicide shots are angled slightly upward.
Number of shots fired: After one shot, even if a suicide victim isn't dead, he would likely be unconscious or physically unable to fire a second time. Multiple shots usually indicate homicide.
Presence of gunpowder residue on victims hand: If a man shot himself, there would be powder residue from unburned carbon on the hand that fired the gun.
Shots through clothing: A suicide victim will rarely shoot through clothing. If he shoots himself in the chest, which is unusual, he will open his shirt to expose the skin. Shots through clothing suggest homicide.
History, a note, other factors: If the victim left a suicide note, or was known to have personal problems, or if there was evidence of drug use or drinking, suicide is likely.
Evidence of a struggle: If there are scratches, cuts, bruises, homicide is likely.
How fast a person dies depends significantly on where the wound is located and how quickly he can get help. A shot to the head might kill, or it might not. A shot to the abdomen might take hours to kill the victim, or he might bleed to death in half that time. A gunshot victim can be rushed to the hospital, have a bullet removed from his abdomen, be well on the road to recovery, then die a week later from some unforeseen infection. Anything can and does happen, which makes any scenario you come up with feasible for the needs of your story.