1. As they gained cohesion, the crews came to possess a sense of responsibility and camefor each other and began to regard to themselves as a community ofwith a common destiny.

sense of responsibility alone is a bit vague, it adds a bit more context by adding "for each other"

2. As my own studies have advanced, I have (may be better to add a bit more content into what type of studies), I am increasingly impressed with the similarities between library reading promotion activities and Communication.

I'm not sure what you mean by library reading promotion activities and communication, its a bit vague.

3. Still using textbook dogma to guide the development of libraries will largely trap the library business.

Of course all your sentences are stand-alone so its hard to "correct" them without context because this sentence may be appropriate in the context of other sentences that help to explain more the details.

Judging it as a stand-alone sentence, "development of libraries" is not wrong but its a bit vague, it could mean development of library resources, funding, planning, interior design or it could simply mean the physical development of libraries as in construction...just for you to think about.

In a similar vein, "trap the library business" is not incorrect but is also quite vague with various different interpretations.

I'm not sure if this is the type of feedback you want though, your level is quite advanced so your grammar is quite good I just thought I'd give you my opinion on other areas of improvement.