“No matter what I do” is a dependent clause, so it must be separated from the rest of the sentence by a comma; however, “when considering economies of scale” is not a dependent clause in this case, so it shouldn’t be preceded by a comma. It is instead part of the preceding independent clause, and it can’t be removed from the sentence without losing some of the main idea.

“Being a weak speller” is a modifier that describes the narrator of the sentence, and it is a dependent clause. A comma is needed after “speller.” The semicolon is used correctly to separate two independent clauses without a conjunction here.

In this sentence, “which was capable of producing toxins to incapacitate or even kill a full-grown horse, human, or cow” is a dependent clause. In other words, it is non-essential information that can be removed and still leave a complete sentence; therefore, it is correctly separated from the independent clause with a comma. The items in the list are also correctly punctuated with commas.

Here, “Being an unlikely candidate for governor” is a dependent clause. It relies on the independent clause (the rest of the sentence) for meaning, so it should be separated from that independent clause with a comma after “governor.” The list is punctuated correctly with commas here.

Here, “Even with a combination of whiskey, opium, and assistants” is a dependent clause that depends upon the rest of the sentence (“early amputations were grisly, excruciating procedures that often resulted in infection and death”) for its meaning, so it should be separated from that independent clause with a comma after “assistants.”

“Ever since Joachim quit his last job” is a dependent clause, so it should be separated from the rest of the sentence with a comma. There is also a comma after “career,” as we’re separating two independent clauses with a conjunction (“and”) and therefore we need a comma before that conjunction.

Here, “Above all” is an introductory phrase and a dependent clause, so it must be followed by a comma. The direct speech is correctly punctuated in the original sentence.

The comma used between "wildly" and "when" is extraneous and creates a grammatical error in this sentence. No comma is needed to separate the subordinate clause "when summer vacation arrived once again" from the independent clause "The student body cheered loudly and celebrated wildly." Note that if the order of these clauses were reversed and the sentence began with the subordinate clause, a comma would be needed after "again": "When summer vacation arrived once again, the student body cheered loudly and celebrated wildly"; however, since the subordinate clause follows the independent clause in the sentence as it is given, no comma is needed.

This sentence is a run-on, and should be split into two sentences with the appropriate punctuation, or given a proper conjunction.

Commas can only be used between dependent and independent clauses. When a comma splits two independent clauses, as in this question, it becomes a "comma splice", and is gramatically incorrect. Either a period or semi-colon should be used.