tuyu ga owaru to, sora ga akaruku mieru hi ga huemasu.

No. In this sentence, と is a conditional/time marker, not the and meaning.

梅雨が終わると means:

• when the rainy season ends
• or once the rainy season ends

In sentences like this, A と B often means when A happens, B happens or whenever A happens, B naturally follows.

So the sentence is describing a regular result:

• When the rainy season ends, the number of days when the sky looks bright increases.

Because verbs before conditional と normally appear in plain form.

So:

• 終わると = when it ends
• not usually 終わりますと in everyday Japanese

This is true even if the main sentence ends politely:

• 梅雨が終わると、空が明るく見える日が増えます。

So the pattern is:

• subordinate clause: plain form
• main clause: polite form if the speaker wants to be polite

This is very common in Japanese.

Because 明るい is an -i adjective, and when it modifies a verb like 見える, it usually changes to its adverbial form:

• 明るい → 明るく

So:

• 空が明るく見える = the sky appears bright / the sky looks bright

You can think of 明るく as describing how it looks.

Similar examples:

• 大きく見える = looks big
• 若く見える = looks young
• 白く見える = looks white

見る means to look at or to see in the sense of actively using your eyes.

見える means to be visible, to appear, or to look.

So:

• 空を見る = to look at the sky
• 空が明るく見える = the sky looks bright / appears bright

In this sentence, the meaning is about appearance, not the act of looking.

That is why 見える is the natural choice.

Because each が is marking the subject of a different part of the sentence.

1. 梅雨が終わる

Here, 梅雨 is the subject of 終わる:

• the rainy season ends

2. 空が明るく見える

Here, 空 is the subject of 見える:

• the sky looks bright

3. 日が増えます

Here, 日 is the subject of 増えます:

• days increase

So the sentence is built like this:

• [梅雨が終わる] と
• [空が明るく見える] 日が
• 増えます

This may feel heavy in English, but it is normal Japanese structure.

It is a noun phrase with a relative clause.

The part 空が明るく見える modifies 日.

So literally it means:

• days on which the sky looks bright
• days when the sky appears bright

Japanese does not need a word like when, that, or on which here. The clause comes directly before the noun:

• 空が明るく見える日
• the days when the sky looks bright

This kind of noun modification is extremely common in Japanese.

Literally, yes, it says days increase, but the natural meaning is:

• the number of such days increases
• there are more days like that
• those kinds of days become more frequent

So 空が明るく見える日が増えます means:

• There are more days when the sky looks bright.

Japanese often leaves number of unstated when it is obvious from context.

Because the sentence is focusing on how the sky appears after the rainy season.

Compare:

• 空が明るい = the sky is bright
• 空が明るく見える = the sky looks bright / appears bright

見える adds a nuance of visual impression. It is slightly softer and more observational. It is not just stating an objective fact; it describes how the sky seems to the eye.

In everyday conversation about the rainy season, 梅雨 is most commonly read つゆ.

So here:

• 梅雨 = つゆ

You may also see or hear ばいう in more formal contexts, such as weather reports or technical language, but つゆ is the usual reading for learners to know first.

Because the sentence is presenting events and relationships rather than setting up a broad topic with contrast.

Using が here makes sense because each clause needs a subject:

• 梅雨が終わる
• 空が明るく見える
• 日が増えます

If you changed something to は, the nuance would shift. For example, 梅雨は終わると would sound wrong here. 空は明るく見える would introduce contrast, like as for the sky, it looks bright, which is not the main point.

So が is the natural choice throughout.

The comma in 梅雨が終わると、空が明るく見える日が増えます。 simply marks a pause and makes the sentence easier to read.

It separates:

• the when/once clause
• from the main statement

It is helpful, but not a special grammar marker. You may see the sentence written without it in some contexts, especially in shorter or more casual writing.

Yes, that is a very natural English rendering.

Some possible translations are:

• When the rainy season ends, the number of days when the sky looks bright increases.
• After the rainy season ends, there are more days when the sky looks bright.
• Once the rainy season is over, bright-looking skies become more common.

All of these reflect the same Japanese meaning. The exact English wording can change, but the Japanese structure stays the same.