Rick, you present for my consideration a given situation that incorporates aspects related to the areas of theology, philosophy and science. Your motivation is testing my ability to develop a line of reasoning that you relate to me as a philosopher of science.
Specifically, you wish to observe how Dynamic-Scientific Philosophy (D-SP), my personal way of analyzing all that exists, tackles the questions you pose.

I gladly accept your challenge, which gives me a chance --as usual with you-- to practice my analytic capabilities, greatly enhanced since I entered, unwittingly, the realm of D-SP.

As is my wont, each paragraph will be commented separately.

Jacob, the following is a completely possible series of events.

1.- You decide to walk somewhere, and just before you take your first step, you decide to pick which foot to start out on.

*1). The situation of "deciding" already presumes a capacity to take decisions. Let us better say that I had to go to a given place at that moment. But, when I have to choose which foot to start out on, I am evincing a way of thinking and acting related to an obsessive-compulsive behavior (OCB). Such relatively common situation --where the right ("correct") foot is usually chosen-- is, of course, a ceremonial dictated by religious archetypes of propitiation. I suggest reading ARCHETYPES.

1a.- You choose your left foot.

*1a).- Perhaps I am rebelling against my compulsive thinking, which my mature mind finds ridiculous.
But let me add that all I've said has nothing to do with the presumed purpose of this exercise in casuistry, to wit, a Jesuitical 'probabilism' vs. a Jansenist strict interpretation of moral choice.

2.- You take your first step, and unbeknownst to you, your foot kills several extremely small dust mites that are living on your floor. One of these mites is crawling in a direction that would have taken it towards a small spider which is almost dying from starvation. The mite would have given it enough nourishment to live another week.

The spider will die and will never get a chance to build a web in the corner of your room where a week from now a mosquito is "scheduled" to be captured by the spider.

That mosquito is going to be carrying a deadly virus, and two weeks from now that mosquito, because it will not be eaten by the spider, will infect nine people with this virus.

*2a) Rick, please note that you do not care the least about the mite as a sacrificial victim. You end this compactum with "people," making it clear that you actually do not care about the insects except for their role in a chain that ends with what might happen to specimens of Homo sapiens, toward whom you are biased. They represent your 'group,' as explained in THE BAD AND THE GOOD.

Jain beliefs, so influential on Ghandi's non-violence preaching, are atheistic --actually non-anthropocentrical-- while you are writing with the anthropocentrical bias developed by H. sapiens' 'buddy' slant, reified as 'Judeo-Christian' doctrine.

Elohim, the universal God of Creation, creates ADAM (=MAN, the first human male) and then his helper CHAVA (Eve=creator of life). As her Hebrew name implies, Eve was already planned --before the apple event-- as the future maker of babies.
The name Chavah (JVH) is, since the inception of Genesis, an etymological cognate of Elohim's future Israelite name (YHVH).

The root of YHVH is HVH, the letter Y being an addition. It is related to 'being' and to 'existing.' The first H is modified to J (having a very similar configuration), creating the meaning of 'living.'

At the same time, Elohim declares that all other creatures were created for Adam and Eve (and, of course, for all already planned future generations).

3.- What would I say to one of the infected persons if by some happenstance it were completely proven to both of us that I could have prevented it from ever happening?

*3).- I do not know; but if I were in your position, I would say that "I'm sorry, how could I have known? Next time I'll do better, cross my heart."

3a.- How do I feel about causing something quite negative to happen that is completely beyond ordinary human ability to foresee?

*3a).- If you feel very bad for a long time, you definitely suffer from the OC syndrome, and quite possibly your brain neurons are underproducers of the neurotransmitters serotonin and norepinephrine.

3b.- What amount of vigilance must I maintain to feel free from any moral responsibility from being the start of a series of events that ends up negatively? How far do I have to see into the future? Do I take risks that are more easily foreseen, that I would ordinarily not take if I thought a bit about it?

*3b).- If you do not follow the advice of looking for medical advice, leading to the prescription of one of the new serotonin-epinephrine enhancers, you probably will enter a worsened state of depression.

3c.-If I were ABSOLUTELY CERTAIN that every time I took a long walk, something negative would occur after a very long chain of events (weeks later and dozens of events removed), would I still walk?

*3c).- You can be sure that according to the laws of probabilities, something bad (and also good) is bound to result. You do not care about the positive results of your actions, because you are obsessed and compulsed by the 'bad' results. You suffer from a condition that is determined by a biochemical defect.

Neurotic manifestations will ensue because the neurons that play the role of superego in the "morality center" are incapacitated, and therefore experiences that might have been dealt with appropriately, are classified as inimical and unsolvable, their memories being then stored in the banks of the repressed memories (the neurotic unconscious). A super-developed moral center compounds the problem, as discussed in CRIME AND PUNISHMENT.

4.- What is negative? How do I decide if the persons that were infected did or did not "deserve" having the virus?

*4).- If sufficient time elapses, each one of them will happen to have initiated a "negative" (as well as "positive") chain of events, even if he has no descendants. But H. sapiens tends to think of rather immediate consequences, for absolutely valid reasons. Each battle-tested person (like myself) knows that feeling heroic or frightened depends on many variables, and that a person's courage cannot be judged on a casual act.

5.- How do I know when to intervene with the destiny and fate of another person?

*5).- As a war medic and as a physician, I happened to enjoy the fortune of not having to criticize myself (and of being commendended). Some aspects of your question are dealt with in FREE WILL, where D-SP shows that exercising free will means consciously acting against one's best judgment.

6.- I could be of some help to almost everyone I know, but I do not do so because there would not be any time left to do anything else; what is my criteria for overcoming this impasse? How do things get to my "front burner"?

*6).- You cannot know that you really will do something helpful to the other in the long run. Just do what looks fair to both. Get some uninvolved friend to help you decide, even by just listening to your own arguments. There are too many variables involved in any decision --that is, for getting the matter to your 'front burner.'

7.- Why do I feel responsible for my actions when they are almost entirely created and carried out by automatic processes? When I accidentally break something of someone, why do I say, "I'm sorry"?
Why do I feel "ownership" of my actions and their consequences in the short term but do not do so for the longer term?

*7).- It would be trite to talk about existentialism, moral imperatives, superego and brain's moral center.
Therefore, I refer you again to THE GOOD, because all living organisms, including single cells, are under the evolutionary imperative of acting for the good of the group, as described by D-SP. A scientific backing of that imperative is described in the essay Anoikis and Apoptosis.