A wWonderful Night A Wonderful Night

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

Sounds more natural than "half a month"

It has been raining for about half a month. 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. It was cloudy and cool at dusk, so it was a good time to exercise.

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

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

ToShould I play basketball or ride a bike? Should I play basketball or ride a bike?

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

Just "ride" by itself is ambiguous

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

I wanted to connect with the nature. I wanted to connect with nature.

I wanted to connect with the nature. I wanted to connect with 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 havout taking a walk as well. There were a few people out taking a walk as well.

There were a few people havingon a walk as well. There were a few people on a walk as well.

"Having a week" sounds odd.

WThe wind was blowing softly. The wind was blowing softly.

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

Sevaeral bamboo branches had been bendingwere bent down, with drops hanging off them, like a rainbow. Several bamboo branches were 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. After I left the town, there wasn't anyone in sight.

"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. What I saw and heard was nature itself.

What I saw and heard were theas nature itself. What I saw and heard was nature itself.

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

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

It was so peaceful that I was delighted. It was so peaceful that I was delighted.

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

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

After coming back, I ate a half -frozen watermelon whilen reading a novel. After coming back, I ate a half-frozen watermelon while 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 my drums, and madenoticed a small improgressvement in my playing. Then I played my drums, and noticed a small improvement in my playing.

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