A wWonderful Night

It has been raining for about half a month.

This is correct, but "It has been raining four about two weeks" sounds more natural. People don't say "half a month" all that often.

It was cloudy and cool at dusk, so it was a good time to exercise.

These are both independent clauses, so you need a coordinating conjunction ("so") to connect them.

ToShould I play basketball or ride a bike?

I thought for a while and decided to ride my bike.

I wanted to connect with the nature.

"Nature" is uncountable if you're talking about plants, trees, animals, scenery, etc.
https://ell.stackexchange.com/questions/153155/the-nature-vs-nature

There were a few people havingon a walk as well.

"Having a week" sounds odd.

What I saw and heard were theas nature itself.

More nature: "All that I saw and heard was nature itself."

It was so peaceful that I was delighted.

More natural: "I was delighted by how peaceful it was."

After coming back, I ate a half -frozen watermelon whilen reading a novel.

A half-frozen watermelon = a watermelon that is a little frozen, but not completely (an entire watermelon!)
Half of a frozen watermelon = one half of an entirely frozen watermelon

Then I played drums and made a smalllittle progress (in learning a rhythm?).

It has been raining for about half a monthtwo weeks straight.

Sounds more natural than "half a month"

It was cloudy and cool at dusk, so it was a good time to exercise.

ToBut I had to decide, should I play basketball or ride amy bike?

I thought for a while and decided to ride my bike.

Just "ride" by itself is ambiguous

I wanted to connect with the nature.

There were a few people havout taking a walk as well.

WThe wind was blowing softly.

Birds were eitherout, some flying in the sky orand others jumping on the road.

Sevaeral bamboo branches had been bendingwere bent down, with drops hanging off them, like a rainbow.

Not sure what you mean here, are the drops like a rainbow or the branches are like a rainbow?

After I left the town, there wasn't anyone in the fieldsight.

"in the field", which field? You could say "anyone in sight" to express that you did not see anyone around you after leaving the town.

What I saw and heard were theas nature itself.

It was so peacefuldelighted by the fact that Iit was delightedso peaceful.

After coming back home, I ate a half frozen watermelon whilen reading a novel.

Then I played my drums, and madenoticed a small improgressvement in my playing.