"To the death" means to persist until the point of death of the person taking the action. It is something you do willingly, it is not done to you, and carries the implication of self-sacrifice. The action in question may or may not be the cause of death. Sometimes you it is written as "to the end" or "to the bitter end;" these are synonymous. The phrase "to the death" rarely has a metaphorical meaning. (I say rarely but I can't think of any.)
"To death" is a variant of "unto death," and means that the action is the cause of death. It is generally not something a victim chooses willingly, it is something that is done to them.
"To death" is also a playful and informal way to say "extremely," or when using death as a metaphor for an end-point or a cessation.
To "love something to death" is to love very much, and is often used playfully and affectionately. Saying I "just love you to death" can come across as cute. Actual death is not implied. On the other hand to say "literally love to death" means that love was the cause of death; similarly to "love to the death", to "love until I die", or to "love until the bitter end" refers to loving until the day of my actual death.
To "starve to death" is to die as a result of starvation, while "starving to death" is a common idiom meaning very hungry. Both can be used for either meaning, but these are the usual constructions.
"Bleed to death," "starve to death," "burn to death," and "beat to death" all mean death due to a specific cause, while "done to death" refers to murder by an unspecified means. Notice that these all refer to violence or deadly situations, and are almost never used metaphorically.
The construction "half to death" means you endured some condition like bleeding or starving, but did not actually die. It is often used to exaggerate a minor incident like hunger or a small wound but which was not actually life threatening. "Beat half to death" and "beat to within an inch of my life" both mean a very severe but nonfatal beating.
"Love to death" means extreme love, "Bored to death" means extreme boredom, "scared to death" means extreme fear, and "sick to death" means extreme disgust. You can often tell by the context; boredom or fright do not cause death, so you know it is a metaphor. These constructions also usually have an object: "scared to death of X." If preceded by "literally" it means someone died in an ironic way that is usually only a metaphor. If he was "literally scared to death," it means it is ironically true; his extreme fear caused a heart attack and he died. Sickness could be a cause of death, but "sick to death" is always a euphemism, while "deathly sick" or "sick unto death" means you are so sick you are going to die.
"Arguing to death" means to carry an argument to and typically well beyond its conclusion. It implies stubbornness, bitterness, or thoroughness. Rehashing an argument that should already be finished is also called "beating a dead horse". On the other hand "arguing until you're blue in the face" means you spent all your breath arguing, and death is implied. "Arguing to the death" means to argue until the day you die; not that the argument kills you, just that you continue for the rest of your life.
To "drive a car to death" means to use it until it breaks down (dies).