Questions about example sentences with, and the definition and usage of "Raining"

A: it's means theres very HEAVY rain!

lots of water pouring down!

A: “Reigning in” means limiting or controlling something by putting restrictions on it.

Reigning in the tech giants as they grow ever more powerful =

Put limits on the big tech companies because they ccontinue to become more powerful.

A: something that you say when it is raining heavily

A: It's an expression which means that there's heavy rain.

A: raining cats and dogs, this expression means it raining heavily

雨が激しく降っています

A: × Raining today,I went to an indoor shopping mall with my family.
✓ It was raining today, so I went to the mall with my family.

× It was good time as I could buy what I wanted before and my son looked like happy a lot of walking.
✓ We had a good time there. I bought some things that I wanted, and my son was happy with all the walking.

This is probably how I would say what you wrote, but it's not an exact translation, since that wouldn't sound as natural.

A: 1. I get depressed when it rains.
2. Rain makes me depressed.

A:
Sentences have to have three words.
If you wanted to you could probably say:
It is raining. I want to sleep. But I slept too much today.

A: Rain is normal during this season in Japan because it's the rainy season.

"Rain" (verb) already has a noun, in fact it's the same word, so you don't need to use 動名詞.

"In this season" is usually ok, but using "in" twice is a bit strange.

There is only one rainy season, so you need "the". The other seasons (Summer, etc.) are proper nouns, so they don't need it.

A: I would say: Rainy day.~
Or: It's raining today.~