回答

文章の構成はよく出来ていると思いますが、所々に綴りのミスや構文の文法的な間違いが見られます。
いくつかの修正をすれば、もっと分かりやすい、伝わりやすい文章になります。
参考にしてください。

I agree with the idea that the legal age of majority should be [lowed] to 18 years old.
→ I agree with the idea that the legal age of majority should be [lowered] to 18 years old.
Firstly, young people should be more responsible to their behaviors and statements.
→ First, young people should be more responsible for their behaviors and statements.
※firstly, secondly, thirdly:通常3つ以上の内容を列挙する時に使う be responsible for … …に対して責任がある
These days the number of crimes by [teenageers] is increasing, and [quarrelings] on SNS seem to [be occered] ceaselessly.
→ These days the number of crimes by [teenagers] is increasing, and [quarrels] on SNS seem to [occur] ceaselessly.
I think, once the age of majority is [lowed], these meaningless cases are less appeared in public.
→ I think once the age of majority is [lowered], these meaningless cases would appear less often in public.
Also, this idea will make our society more flexible and diverse because of the increase of the [propotion of erection]??.
→ Second, this idea will make our society more flexible and diverse because people who vote in election increase in number.
2番目に、この考え方だと、選挙で投票する人の数が増えるため、私達の社会は今よりも柔軟かつ多様性があるようになるでしょう。
The opinions of young people will be more [refrected] on the politic.
→ The opinions of young people will be more [reflected] in the politics.
若者の意見が政治にもっと反映されるでしょう。
Therefore, this idea will give young people personal responsibility and the chance to make a better society. 〇
→ ◎ Therefore, this idea will give young people more personal responsibilities and chances to make our society a better one.
従って、この考え方(成人年齢の18歳への引き下げ)は若者に、我々の社会をより良いものにするためのより多くの個人的責任、及び機会を与えるでしょう。

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