It is correct, but be careful! "can't not" means "must" or "have to". It does not mean "can".

I apologise. I have been writing in a confusing way. I will be more clear. "At the same time" has two meanings. The first meaning is "at this time" or "at this date". The second meaning of "At the same time" is "nevertheless".

I don't think so? You said "At the same time" is saying that the times of the publication are the same, except for the year being 20 years later. I responded that no, I think it is the secondary meaning that is intended, which oxforddictionaries and thefreedictionary define as a synonym of nevertheless.

I utterly disagree with you here. oxforddictionaries supplies the definition: Nevertheless (used to introduce a fact that should be taken into account): I can’t really explain it, but at the same time I’m not convinced; thefreedictionary supplies the definition Fig. nevertheless; however; along with that. Bill was able to pay for the damage. At the same time, he was very angry about the accident. We agree to your demands. At the same time, we object strongly to your methods. The use of the word but heavily implies that it is this definition that the author is after.

Here is an ngram showing the frequency of these suggestions.

It does not sound idiomatic to me. I would use a single adverb. "Badly" is a good word for this context. "They are badly neglecting their duties," is common.

Sprawling cities often have low population density and short buildings.

Although B is not grammatical, it is used by English speakers. Jim Reynolds implies this when they say that it is used in casual speech, and very informal writing. But I suppose Lambie is correct. As written, B is not considered correct in formal written contexts.

"Looking for development of your skills**?**" sounds strange, but it is okay. "Looking for skill development?" is more natural. "Looking to develop your skills?" is the most idiomatic way to write this.

In Australian English, we say "pat". In American English, "pet" is most common. In British English, "stroke" is most common.