These days, bullying is one of the most serious problems in schools in japanJapanese schools, and we must stop it right now.

This sounds better to me since we’ve avoided the repetition of “in.”

The main cause of bullying is differences between students.

This makes the meaning clearer.

Those who are bullied usually seem to have something different from others’, such as their habits, personalities, or maybe skin colors.

“Skin color” doesn’t seem to be used in the plural much.

Bullies are just trying to find something different about them andose whom they bully and are not aware that they themselves are also very different from others.

I prefer repeating the “are” as the structure isn’t exactly parallel: in the first part, “are” is part of the present progressive, whereas in the second, it’s just used as a normal “be adj.” construction. The wording otherwise seems okay, but I added in details for clarity.

They are usually aware that something not goobad seems to be happening, but they often ignore it if it is not obvious, because coping withhandling it is troublesome.

“Untoward” might also fit, although it’s more specific than “bad.” “Not good” isn’t so common in formal writing.
“Coping” is more a passive action that someone who is suffering does. Examples:
- She couldn’t cope with the bullying at the girls’ school, so she had to transfer out.
- He learned to cope with his anxiety after regular meetings with a mental health professional.

So it is always important for teachers to actively learn about, and try to solve problems in their classes.

They are part of the same clause so we don’t need a comma.

These days, bullying is one of the most serious problems in schools in jJapan, andtherefore we must stop it right now.

Japan is a country (proper noun), so it should be capitalized.
I changed "and" to "therefore" because this is a cause and effect sentence.

The main cause of bullying is differencesversity in people.

Those who are bullied usually seem to have something different from others’, such as their habits, personalities, or maybe even skin colors.

Bullies are just trying to find something different about them and not one dissimilar from them to harass, while being unaware that they are also very different from others.

I changed "different" to "dissimilar" to avoid being repetitive, so I also had to change the sentence a bit. You should add "to harass" or "to torment" at the end, because you need to say what the bullies are doing.

They are usually aware that something not good seems to be happeningthere is a bad situation between students, but they will often ignore it if ithe bullying is not obvious, because coping with it is troublesome.

Changed the sentence a bit to make it sound smoother.
You pretty much never need a comma before "because"

So, it is always important for teachers to actively learn about, bullying and try to solve problems in their classes.