It is quite common to have a bad situation, however, nowadays there is
an intense debate about [whether it is better to keep trying until
obtaining what you want, or just to accept the things as they are].
Yes, it's correct.
"Whether" is an interrogative (question) word introducing the bracketed subordinate interrogative clause (embedded question) ...
Bryan Garner, Garner's Modern American Usage, second edition (2003) answers this question in a consistent way that is easy to apply to particular instances of "whether (or not)":
Whether or not. Despite the superstition to the contrary, the words or not are usually superfluous, since whether implies or not—e.g.,:
"In another essay, 'The ...
Usually when using the word whether in a sentence, the or not is superfluous (i.e., not required). However, when whether or not means regardless of whether, the or not part is required.
Examples of when or not is required:
The postman will deliver my mail today whether it snows or not.
(…regardless of whether it snows.)
The former CEO of Global Bank is ...
You're focussing on the wrong thing. "About whether" is not a constituent; it's not a phrase, or a clause, or a construction. It's not anything by itself and for sure there's no rule about it. It's just two words that happen to occur together in a sentence. Both of them introduce constituents, and those constituents are stacked inside one another ...
I believe all are correct but perhaps a bit stilted, or less than comfortable.
It would be more natural to say Whether to kill him or keep him. The missing to would certainly be understood. This would be common for spoken English or written as a quote from someone. Perhaps you should ask him. He may have a better answer.
The repetition of whether in interrogative content clauses (where whether could be replaced by if) is unnecessary but grammatical. Fowler's Modern English Usage (p696) has an example:
I cannot remember whether they were lowered into the street or
whether there was a window opening out at the back.
"Whether is often repeated as a clearer ...
An interrogative whether clause in adjunct (modifier) function doesn't necessarily need "or not". Compare:
They will play tomorrow whether or not it rains.
They’ll complain whether we play tomorrow or at the week-end.
"Or not" only occurs in the first of those two examples; nevertheless both whether clauses are adjuncts (modifiers), more ...
Your question is not just about whether and if, but also about the correct tense to use and about appropriate politeness.
'I was wondering if...' is a good example of a polite request. Past continuous tense to indicate distance, indirectness (and thus politeness):
e.g I was wondering if I could take the afternoon off', said to a superior.
'I was ...
For usage, I suggest you look in a dictionary that has example sentences, not a grammar book.
I find that Oxford gives lots of examples, so that will be my starting point.
1 Expressing a doubt or choice between alternatives.
‘he seemed undecided whether to go or stay’
‘it is still not clear whether or not he realizes’
Although both if and whether can elicit binary answers, if strongly references one option (the stated option) whereas whether references both.
The proposition "I sit next to you" has an implicit negation: "I don't sit next to you". The question "Do you mind?" with reference to this proposition could have 4 possibilities:
I mind that you sit next to me.
Whether to kill him or to keep him is a phrase that functions as a subject in 1 and an object in 2.
Whether to eliminate the second to in the phrase is a matter of style.
But 3 is incorrect. The phrase is unattached to anything; it would be grammatical if it were changed to whether we kill him or keep him.”
All answers are valid, but the third reduces redundancy and makes the sentence more concise than the others. (The second "whether you're..." is implied.)
An alternative formulation might be:
I can offer a comprehensive solution to help you succeed, be it big or small.
I have difficulty understanding what is supposed to be big, small,rich or poor. The ...
We use "if" or "whether" to introduce clauses after verbs of doubting:
I don’t know if I can drive. My foot really hurts.
Look at If or whether: indirect questions at the Cambridge Dictionary.
I don't know whether he is right or not
I don't know whether he is right or wrong
The sentences I wondered whether his genius was governed by his mood and I wondered whether his genius wasn't governed by his mood say essentially the same thing. They are not opposites.
However the second uses the negative in order to emphasise what a remarkable proposition it would be, that someone's genius be governed by their mood. So remarkable that ...