'But' is a conjunction that is used to introduce a statement or clause that will be in contrast or different from what has already been mentioned.
'And' is a conjunction that is used to connect statements or clauses that are similar.
In your example, the conjunction 'but' would be better. The speaker is contrasting disciplining a preschooler with being ...
Well for a start it’s direct speech, so pretty much anything goes. But even given that, I’d say it’s perfectly fine. You could view it as a prematurely terminated list, where it’s being suggested that the speaker was planning to describe a four-item list:
Okay, I am gonna look around, take a few statements, worry a few suspects and generally put the fear ...
There is always another alternative, regardless of it being explicit or not.
He called to check whether she was okay. (or not okay)
She didn't know whether to continue with the plan. (or not continue the plan)
The sentence is comprehensible as you have written it, but I would say that “They are British; so am I.” is more natural/strictly correct.
If you want to use a comma rather than a semi-colon, “They are British, and so am I.” would work.
Not only X, but also Y
The word “do” will be very useful here. If you remember the three forms that the present tense can take — “I run, I am running, I do run” — then you’ll recognize the proper use of “do“.
Not only do institutes provide X, they provide Y.
Not only does the hotel provide X, it provides Y.
Not only does the hotel provide ...
As the days passed, the nation grew increasingly sceptical [that any of
the minors had survived] - let alone all of them.
Syntactically, the bracketed content clause (your that clause) functions as complement of the adjective "sceptical".
Semantically, "sceptical" has two arguments, expressing the nation's state of mind relative to the proposition that ...
This is a very common structure:
I am happy that you are happy
I am sure that you are wrong
I am skeptical that this is a good idea
In US English, "that" is frequently omitted. In British English, "that" is much more common.
I am happy you are unhappy [AmE]
To British ears, it can sound ambiguous, and we might well say one of the following two:
I am ...
You pretty much answered your own question when you said you assumed it means the nation grew sceptical about the possibility that the minors had survived.
It could be written:
...the nation grew increasingly sceptical of the fact that any of the minors had survived.
With these words added you can see the function of "that" more clearly. It is the fact ...
In answer to the question as you originally wrote it: yes, you can omit the coordinating conjunction, "and" and still have an idiomatic, grammatical sentence.
Sentence 2 can be correctly rewritten as sentence 2a.
Sentence 1, as you originally had it should have had a pair of commas to set off the parenthetical remark, "but nevertheless interesting". In ...
Because none of the others result in a grammatical sentence.
Gilbert Stuart is considered by most art critics that he was greatest portrait painter North America contains.
"that he was greatest" does not work, neither does "is considered ... that"
Gilbert Stuart is considered by most art critics as he was greatest portrait painter North America ...
How have... is a question whereas How... is a statement.
How have health care monitoring devices helped in changing your life?
Is asking the audience to answer. Whereas:
How health care monitoring devices have helped in changing your life.
Might be the title of the paper in which you discuss the findings.
It's not easy to parse because it's such a long clause, but i think
When people tell you to settle down and stop dreaming but you know what you love, you should stay true to yourself and keep going.
is correct, because 'but you know what you love' needs to be included in the same subordinate clause as 'when'.
'When ..., but when...,' seems wrong to me.