Both are ok. I prefer the first, with a single indefinite article. The only issue is with "oligarchy." I think for consistency, you should change it to "oligarchic." (Make them all adjectives).

The first two are perfect. The third is perfect, but the parentheses should be (at work). If it's happening now (progressive), make it "are screwing up," and if you're talking about the work day that is over, "we all screwed up." Depends on your meaning. The fourth: this is an old, even antiquated use of the word "screwed" that you will probably only see in literature. "Screwing up" eyes doesn't really help anyone, so it isn't really correct. Remove "to help" and it's correct, but remember that this is an old usage and you probably won't see it anywhere. Don't say it, it will confuse people. Can just replace with "She looked up." The fifth: "Mary screwed up her friend's full name." The sixth: "screwed up" is used right, but the sentence doesn't look right. I would change to," What happens when you screw up is that you get discouraged," or "You get discouraged when you screw up." But don't get discouraged! You're doing great. The seventh: Pretty good, I would simply change "admits" to "admitted" and "so" to "and."

"Come to an end" refers more to an event or a process. You would say "Slowly the day was coming to an end," not "the end." The difference is slight, but most of the time you will want to say "come to an end," not the other. A correct example for each: His life has come to an end. He has come to the end of his life. Again, the first is better.

Both of those are correct, and both are common, but they have two somewhat different meanings. You already know that one is a verb (a week to process) and one is a noun (the process takes). "Around here" doesn't really seem to fit, and I don't think you need to add anything to those two sentences. They are complete and correct.

It is always proper to use the capital I. Always, no exceptions. The lowercase i is used only in informal writing, like in text messages. It is best to always use the uppercase I.

I am a native speaker (U.S.) and have never heard anyone say "bolster up" for any reason. I would avoid it (unless you are working in the construction industry) and just use "cheer up".

Usage is only ever a noun, and refers to the "how" something is used, especially in terms of a customary or ongoing normalized use. "Use" can be a verb or a noun, and "use" in its noun form is much more common than "usage." When in doubt, stick with "use." This is a very advanced question and difficult for even a native speaker to answer!