Hokkaido, at Japan’s northern end, getis barely affected by the rainy season.

"Gets" is okay but slightly too overly informal for my taste when used with "affected." But I think the other suggestion, to move "barely" before the verb, would also make it better.

That's why these days, it's raining every day in these days.

It's already correct if you remove "in," but the repetition of "day" doesn't sound as nice.

Although most of people don't like rain, I like rain.

I would also replace the last part with "I like it" or "I do" to avoid repetition.

In Japan, there is a season called “Tsuyu”, which means “rainy season”.

Comma isn't necessary in this sentence.

It starts in the beginning of May from the southernmost tip of Japan in Okinawa, at the beginning of May, andnd in June slowly moves north over the rest of Japan in June.

Also a stylistic choice/your sentence is grammatically correct, but to a native English speaker it sounds more natural putting time before location.

Hokkaido, at Japan’s northern end, gets barely gets affected by the rainy season.

To an English speaker, putting "barely" in front of the verb sounds more natural.

That's why it's raining every day in these days.

Although most of people don't like rain, I like rainit.

It's a small correction, but replacing "rain" with "it" in the second clause makes the sentence less redundant. However, it's a stylistic choice and would still be correct if you kept "rain".

In Japan, there is a season called “Tsuyu”, which means “rainy season”.

It starts fromat the southernmost tip of Japan in Okinawa atin the beginning of May, and slowly moves north over the rest of Japan in June.

That's why it's raining every day in these days.

Although most of people don't like rain, I like rainit.

Strictly speaking, I like the smell and the air after the rain.