I was pleased to know the differences between 'in the end' and 'at the end'.
In the end, everything is going to work out.
He usually does that at the end of every month.
Now, I do wonder if the same principle can be applied to 'beginning'. I mean, what's the difference between 'at the beginning' and 'in the beginning'?
These are examples I got from the Corpus of Contemporary American English:
... you put in $10,000 in the beginning of last year ...
I mean, I know that she was appointed in the beginning, but do you know where she is?
It happened in the beginning of a time in history we call the Civil Rights Movement, when people fought ...
And President Obama referenced that line at the beginning of the speech last night...
I will go back to say what I said at the beginning of the year, there is great and powerful evil, but there is great...
And you explain your motivation at the beginning of the book, that you wanted to help them make sure that your father...
There are about 3500 entries for 'in the beginning' and 7000 for 'at the beginning'.
Well, there's this famous one: "In the beginning, God created the heavens and the earth" (Genesis 1:1.)
I would use it as another way to stay "when things first got started," without a reference to exactly what was getting starting.
However, I would not use it the way it is shown in your first and third example. If I am stating WHAT was beginning (the civil rights movement, the year), I would use "at."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.