We can't get a new close reason without deactivating an existing one or petitioning the CMs to give us another slot. In order to do that, there needs to be a large number of posts that have been closed with a relevant custom close reason ("I’m voting to close this question because..."). For high rep (10k?) users, these stats can be found under Questions closed with community-specific reasons. I tried to count how many of the closures in the last 90 days could have fallen under your proposed close reason, and I counted less than 10, maybe slightly more if "because it looks like a peeve" fits. That's simply not enough in my opinion to warrant a new reason.
Reviewing your proposed examples:
Why did Shakespeare use "songs" in Hamlet: "The songs and arrows of outrageous fortune"? — Close as "unclear what you're asking" and leave a comment asking where they got that quote from or if that's a typo.
"A bucket full of twigs" is a common phrase ... — This depends on the context of the rest of the question. Does it contain enough details to answer? There are some expressions that are regional, rare in printed sources, but very real otherwise. Or maybe they heard it twice, which isn't a lot but... We don't really care about the author's (or your!) opinion of what is common.
I have learned that we cannot use an adverb after the verb "to be" ... — This is a common type of question across all of Stack Exchange, so common that jargon has developed around it. People often don't know enough about the subject in their questions to know what advice is bad and what's not — that's why they're asking instead of answering. This type of question really needs a frame challenge as an answer. (Since we are a site that gives out information rather than life advice, frame challenge answers are easier to pull off here too.)
Similarly, when I was reviewing the list of actual close reasons, I noticed several that look like they shouldn't have been used, but it's hard to track down what questions they were used on.