Learn English – Are there words that are spelled the same but pronounced differently depending on whether the initial letter is capital or lowercase

I hope I can answer at least part of your question, and with luck perhaps assuage your frustration to some small degree. You asked about origins:

Lose comes to us from Old English

ORIGIN Old English losian [perish, destroy,] also [become unable to find,] from los [loss.]

Choose comes from the same language:

ORIGIN Old English cēosan, of Germanic origin; related to Dutch kiezen.

In Old English, losian would have sounded something like LOH-zee-ahn, while cēosan would have sounded like CHAY-oh-zahn. Both these words are in infinitive form, and would have different conjugations.

In Middle English, losian became losien and cēosan became chesen or chosen. Now, the double-o construction, seen in words like choose and boot, originally indicated a long vowel sound, which itself originally meant literally a long vowel sound, i.e. one that was held for a longer period of time. There weren't any markings to indicate duration, so an extra letter was added to indicate that a word like boot should actually be pronounced the way we pronounce boat today — exactly analogous to German's pronunciation of das Boot, which does not sound like something one wears on one's feet.

But there was another Middle English word for lose, which was leosen (from OE lēosan), and it's not clear if our current word has a single ancestor. Possibly a merging of the two histories resulted in the pronunciation we have today.

Now, I wish I could draw a clear line for you that brings us from past to present and illustrates why today choose and lose and even whose perfectly rhyme but dose and moose do not, and why we pronounce close (meaning near) differently from close (meaning to shut), but the plain truth is I'm just not that smart. English pronunciation is quirky and peculiar in ways that defy description, much less understanding. If there were anything at all to be done about this, we would have an intolerable situation on our hands; but as there is nothing we can do about it, the situation must be endured. Be comforted by the belief that all these pronunciations will change in time — although to what is not at all clear.

I'll leave you with an old joke, and hope you can put aside your frustration long enough to laugh at the pronunciation and spelling mess we have inherited.

Q. How do you spell fish?

A. Ghoti! Just use the gh from rough, the o from women, and the ti from action (or ration or station or — well, you get the idea).

[Source for the above etymologies: Origins: A Short Etymological Dictionary of Modern English, by Eric Partridge]

According to Steven Pinker, in The Stuff of Thought:

Homonymy usually arises when an ancestral word budded off new senses in a language's history and current speakers retain no inkling of the original connection. For instance, the word odd originally referred to something that stuck out, like the point of a triangle. Then it was extended to refer to something that metaphorically stuck out because it was unusual, and then was extended further to refer to a number that had one unit sticking out from a pair.

Homophony, on the other hand, is defined as a phenomenon

in which distinct words are pronounced the same way, usually because their original pronunciations got merged in the history of the language. For example, four and fore sound alike today, but four originally rhymed with tour, and fore originally rhymed (more or less) with flora; we see fossils of the old pronunciations in the way the words are spelled.