I'd find better words to replace these:

excerpt (whether it's spelled correctly or not)
-excerpt--> anecdote
impede
-impede--> prevent
regret (which needs a direct object after it)
-regret--> regret IT

The verb tense and word choice in this sentence need fixing. It's an example of non-standard English use that'll stick in a reader's mind as a negative.
He could have checked the dog and see if it is...
-He was able to check the dog, but he did not do it.

These are incorrectly used dashes; you have created run-ons here:
...difference--he...
...on the individual--he fell and was injured.
- So periods are needed?
...difference.He
...on the individual. He fell and was injured.
-Dashes replace parentheses and add emphasis, right?
-How come they don't work here?

At first you write that it might have happened, and then you write that it did happen. This is a classic example of wordiness. Get rid of the "might have" and put the two sentences together:
...and it might have been possible that some kid run into him and cause him to fall. Shockingly, it did happen.
-...and some kid ran into him and caused him to fall.

Have you ever ignored someone who needed help and felt guilty afterward? Once there was a man who ignored an injured dog as everybody else was doing. He assumed that it was not injured, but he later found out that the dog had been injured. Fortunately, a lady took it to the vet. She made a difference: She stepped up and saved the dog. Everyone is responsible for other individuals because it can definitely save a life.

Clearly, the man was irresponsible. He could have checked the dog to see if it was all right. Instead, he made an assumption, as everybody else did. He went along with the crowd. At that time, everyone had responsibility to at least check on the dog, but they all acted irresponsibly until the lady came along. Luckily, the dog was rescued, but the man felt guilty for not rescuing it when he first noticed it. The dog could have died. Irresponsibility can result in an individual's death.

On a related note, I was irresponsible during recess. A disabled child was playing basketball, and the ball rolled off away from him. I could have picked it up and handed to him, but instead I kicked it farther away. The disabled child had a leg problem, so walking was quite difficult for him. What made it worse was that at that time the playground was chaotic, and some other child ran into him and caused him to fall. Like the man in the anecdote above, I felt guilty. My irresponsibility had a negative effect on the individual. He fell and was injured.

Everyone is responsible for other individuals, for it is the matter of life. Helping others when they need help prevents us from feeling guilty later on. There is often only one opportunity to help someone, so make it count. Then you won't regret it.

Compare your original with what I have corrected above. Notice the changes in verb tenses, word choice, punctuation, etc.

I'm still unclear where the law is about the underlined statements you make. Who says we must all be responsible for everyone else?

Hyphens and dashes are two different marks of punctuation, and neither can correctly substitute for a period and capital letter when a new sentence is beginning. You can also learn to correctly use a colon or even a semicolon.
~ http://grammar.ccc.commnet.edu/grammar/marks/hyphen.htm
~ http://grammar.ccc.commnet.edu/grammar/marks/dash.htm
~ http://grammar.ccc.commnet.edu/grammar/runons.htm
~ http://grammar.ccc.commnet.edu/grammar/marks/colon.htm
~ " target="_blank">http://grammar.ccc.commnet.edu/grammar/marks/semicolon.htm

To find better words to replace certain terms, you can use a thesaurus. A thesaurus provides synonyms or alternative words that can be used to convey the same or similar meaning. You can either consult a physical thesaurus or use an online version, such as Thesaurus.com or the thesaurus feature on word processing software.

To improve the verb tense and word choice in a sentence, you need to make sure that the sentence is grammatically correct and conveys the intended meaning. In the given example, the correct sentence would be: "He was able to check the dog, but he did not do it." This revised sentence uses the past tense correctly and clarifies the meaning.

When using dashes, it's important to use them correctly to avoid creating run-on sentences. Dashes can be used to replace parentheses or to add emphasis, but they should be used in moderation. In the provided examples, the correct usage would be to replace the dashes with periods to create separate sentences. For instance, "...difference. He" and "...on the individual. He fell and was injured." This helps maintain clarity and correct punctuation.

The last example is an instance of wordiness and can be improved by condensing the two sentences into one. Instead of saying "it might have been possible that some kid run into him and cause him to fall. Shockingly, it did happen," the sentence can be revised as "Some kid ran into him and caused him to fall, which was quite shocking." This revised sentence eliminates the wordiness and conveys the intended meaning more effectively.