Regular Holidays of Beauty Salons

Japanese beauty salons (and barber shops) are closed every Tuesday in the Kanto region, and every Monday in the other regions.

Around the Second World War, Japan had faced a shortage of electricity.

For this reason, Monday or Tuesday had established as Electricity Outage Day, and most electricity supplies had stopped on the day.

On the other hand, electric perms that had been performed in beauty salons needed a lot of electricity.

Hence, beauty salons were forced to be closed on Mondays or Tuesdays.

This custom has remained until today, and there are many beauty salons that close on Mondays or Tuesdays.

美容院の定休日

日本の美容院は、関東では火曜日、それ以外では火曜日であることが多いです。

第二次世界大戦前後の日本は、深刻な電力不足に陥っていました。

このため、月曜や火曜を電力供給をストップする休電日として定めていたようです。

一方、かつて美容院で行われていたパーマは電気パーマと呼ばれ、大量の電機を消費するものでした。

従って、美容院は月曜、もしくは火曜を定休日にせざるを得ませんでした。

この名残から、現在でも月・火を定休日としている美容院が多いようです。

• Around the Second World War, Japan had faced a shortage of electricity.
• Around the Second World War, Japan had faced a shortage of electricity.

  "Faced", already indicates past tense, so you do not need the "had".

• For this reason, Monday or Tuesday had established as Electricity Outage Day, and most electricity supplies had stopped on the day.
• For this reason, Monday andor Tuesday werehad established as Electricity Outage Day, and most electricity supplies werehad stopped on thate day.

• On the other hand, electric perms that had been performed in beauty salons needed a lot of electricity.
• On the other hand, eElectric perms that had been performed in beauty salons needed a lot of electricity.

  Your grammar was good, you just didn't need to say "On the other hand". It is just general writing advice.

• Japanese beauty salons (and barber shops) are closed every Tuesday in the Kanto region, and every Monday in the other regions.
• This sentence is perfect! No correction needed!

• Around the Second World War, Japan had faced a shortage of electricity.
• During the Second World War, Japan had faced a shortage of electricity.

• For this reason, Monday or Tuesday had established as Electricity Outage Day, and most electricity supplies had stopped on the day.
• For this reason, Monday or Tuesday was established as Electricity Outage Day, and most electricity supplies were cut off on the day.

  cut off ≈ turned off ≈ powered off ≈ 電気を消す

• On the other hand, electric perms that had been performed in beauty salons needed a lot of electricity.
• On the other hand, electric perms that had been performed in beauty salons needed a lot of electricity.

• Hence, beauty salons were forced to be closed on Mondays or Tuesdays.
• Hence, beauty salons were forced to be closed on either Mondays or Tuesdays.

  eitherの方はぺらぺららしいです。

• This custom has remained until today, and there are many beauty salons that close on Mondays or Tuesdays.
• This custom has remained even until today, and there are many beauty salons that still close on Mondays or Tuesdays.

  「even」を除くと、今日にあなたはこの仕方を止めたいことらしいです。(文章残りを聞くことの前に)

面白い！
米国には、多いの小さい店は日曜日に閉店する。
チックフィレイは大きなレストランのにまだ日曜日に閉店する。
教会員は日曜日の朝に大会するから。

• Japanese beauty salons (and barber shops) are closed every Tuesday in the Kanto region, and every Monday in the other regions.
• Japanese beauty salons (and barber shops) are always closed Tuesdays in the Kanto region, and Mondays in the other regions.

  This form makes it sound more like something that's been going on for a long time.

• Around the Second World War, Japan had faced a shortage of electricity.
• Around the Second World War, Japan faced an electricity crisis.

  Just an alternative.
  
  About the "had" thing, I agree that it shouldn't be there, but that's not because the tense is already indicated by "faced". The past perfect tense is used for example for actions that took place before some other point in the past we're describing. Confusing? Example:
  
  I went to church. I had cooked the soup.
  
  Meaning: I cooked the soup before going to church.
  
  I went to church. I cooked the soup.
  
  Meaning. I went to church, then I cooked the soup.

• Hence, beauty salons were forced to be closed on Mondays or Tuesdays.
• Hence, beauty salons were forced to close on Mondays or Tuesdays.

• This custom has remained until today, and there are many beauty salons that close on Mondays or Tuesdays.
• This custom still remains, and there are many beauty salons that close on Mondays or Tuesdays.

I'm in awe of your output.