Scientifically we do not have a firm grasp on the nature of death and signs thereof. Once an organism has met the criteria for life, at some point its function tends to decay and ultimately cease. We tend to use cessation of brain activity for legal questions, but there are organisms without brains so that is not a great answer. It may be that death is a concept of our own invention which does not necessarily fit an universally applicable moment in the life cycle of organisms.
Scientifically speaking, a zygote is one organism. As I stated earlier, personhood is a legal term, not a scientific one. When the dividing zygote or morula separates into two populations of cells, the number of organisms increases by one.
"In twins, when does human life of each twin begin?" As I already stated, in the case of identical twins, the transition is made from one organism to two at separation into two (populations). In the case of fraternal twins, each organism comes into being by virtue of an independent process of fertilization.
"When we clone sheep, when does sheep life begin?" The definition of an organism is independent of the method of fertilization or preparation. I can provide links to introductory biology texts if you are curious about what constitutes an organism. A good rule of thumb is that an organism is a cell or multicellular unit that takes in matter and organizes it, maintains homeostasis, and reproduces in some fashion. An ovine entity meeting these criteria would tend to be alive.
"... then how can you not know when human life ends?" Life ends when the criteria for being alive are no longer met. In theory this may be a simple exercise. In reality, it is hard to look at an organism and know when exactly it has completely ceased to maintain homeostasis, for example. All of this is speaking according to accepted scientific definitions, of course. A lawyer or philosopher would have, I doubt not, his own ideas.
"Frankly, I value the life of my dogs more than the lives of the vast majority of the people of the world." I believe you and feel very differently. My beliefs, however, do not change whether an organism is human or whether it meets biological criteria for life. My point earlier was very much in agreement with your sentiments (as I understand them): some people value human life more than others and have various arbitrary or non-universally applicable criteria for determining the value and/or rights of a human life.
"... or just a 2 celled organism ..." BTW, a zygote has but a single cell.
"By the time the zygote [sic] reaches a stage where he or she could live without heroic medical intervention ..." This definition changes based on one's definition of heroic, as well as based on the time and location in which the mother and offspring live.
"Faced with a choice of the life of the mother or the life of the organism growing in her ..." I think most would agree with this notion. A more interesting question is when the convenience of the mother outweighs the life of the offspring.
"What I do not understand is why someone would value a zygote more than a 5 year old child dying a painful death ..." I believe this is a strawman. I have never once seen such an evaluation made, ever.
"So I ask the OP, what is more immoral?" I am not the OP, but an important distinction is that one law deals with whether a given class of humans has the right not to be killed while the other deals with one specific mechanism (not universally agreed as the most effective) for dealing with a problem.