Hello, Need2Know
Sentence #1 is correct. It's not the only option, though.
2. I'd rewrite it as:
"No, he hasn't called on us either this month or last (month). "
3.
"After he began the metting, he said 'I'm going home'."
"After he began the metting he said 'I'm going home'."
4.
"Little Rock, Arkansas, was the scene of tragedy and strife."
5.
"The new machine, which I haven't ever learned to operate, is out of order."
"The new machine which I haven't ever learned to operate is out of order."
In the first case, either the listener knows what machine you're referring to or there is only one new machine.
In the second case (without commas) there may be several new machines and you want to make clear that the machine you're referring to is the one you don't know how to use.
6.
"Did the novelist Ernest Hemingway once live here?"
You don't put "Ernest Hemmingway" between commas if the listener doesn't know beforehand what novelist you're talking about.
On the other hand, if his name has been mentioned before and it is understood you're stil talking about Hemmingway, you could use commas.
I hope it helps. Surely, though, you'll get some different opinions from others here.
Miriam
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I've come back to add something: I've just noticed that "either", in sentence #2, can refer either to time (this mont or last month) or to the people who haven't been called on ("us" in addition to someone else who hasn't been called on either). That would make the position of the comma change.