Well you kind of have epistemology and ethics confused together.
Epistemology is the branch of philosophy that studies the nature and means of human knowledge, e.g. how do we acquire it, how do we perceive reality, how do we judge the truth or falsehood of conclusions, etc.
You have recognized in the first sentence the metaphysical base of Rand’s epistemology, that since reality exists independent of consciousness, existence sets the terms of cognition, and thus if we want to gain knowledge, we must adhere to the standards reality sets. Then, after we are done figuring out what those standards are, and fleshing out the details of the theory of knowledge, we move on to ethics. Ethics is where we run into the problem of an ultimate end, a final goal that acts as a criterion to judge all values. Rand attacks this problem by questioning the nature of values and why they arise in human existence in the first place, and thus discovers that there are inexorably linked to the phenomenon of life. So her ethics are biocentric, as the life of the organism must be its ultimate end. It is then that she examines the nature of man, that it is through the use of his reason that he survives and functions, and so forth. The issue of force only comes into the picture when we look at social ethics and politics as we think about what should be the principles of interpersonal relations.
About the principle of the initiation of force as evil, it’s very easy to understand. Think of it this way: you would have done something different if you were not forced. That’s the whole point of forcing you to do something, i.e. to get you to do something that you wouldn’t otherwise have done, or to get you not to do something that you would have done. In this way, force is aimed at the rational judgment of another person, to force them to act against their own mind. But as we have seen in the Objectivist ethics, we need the judgment of our reason to select the values we pursue. If force interrupts this, then it keeps us from acting according to our judgment, and thwarts our ability to achieve our values.
Here are two good threads on force:
Induction of “the initiation of force is evil”
Reduction of “the initiation of force is evil”
On the connection between egoism and self-interest, there’s not like one case to be made for egoism then a separate case to be made for self-interest, to pursue your rational self-interest is what an egoist ethics mandates. Pursuit of your rational self-interest, pursuing what is beneficial for you, must be the egoist’s “policy” so to speak (obviously, the opposite would be pursuing what is detrimental to you.) So, in this way, egoism is infused with the very nature of a rational morality, in the earlier concepts of life and values that Rand explored. We saw that, if a man wishes to live, his own life must be the ultimate end. The end tells you the standard by which you judge the various means. The standard tells you what “policy” you must take in regards to achieving the end. So if the end is my survival and well-being, then I should work to achieve my survival and well-being, and I should not sacrifice my survival or well-being to the demands of others.
So holding a man’s life as the standard of value necessarily means egoism, because who is the one doing the living in each case? Individual humans, right? In this way, self-interest follows directly from the ultimate end. We can see it makes sense that way, because the ultimate end gives us the standard of value (man’s life qua man), but man’s life qua man is an abstraction that applies to all men as the standard. But the purpose of acting according to that standard is each person’s life, life being the attribute of individual acting men. Each individual’s life is the basic unit of morality, each individual’s life is what mandated the necessity of value achievement in the first place, thus requires a policy of rational selfishness.