Wrzesień bywa ciepły, ale wieczorem jest już zimno.

Yes — month names in Polish are normally written with a lowercase letter: wrzesień, październik, maj.

Here it is capitalized only because it is the first word of the sentence. If the month appeared in the middle of a sentence, it would usually be wrzesień, not Wrzesień.

Bywa means something like can be, is sometimes, or tends to be at times.

So:

• Wrzesień jest ciepły = September is warm
• Wrzesień bywa ciepły = September is sometimes warm / can be warm

This adds the idea that it is not always warm, but that warm September weather happens from time to time.

Bywa comes from bywać, which often expresses repeated or occasional states/events.

Because ciepły is an adjective agreeing with wrzesień.

• wrzesień is a masculine noun
• so the adjective also takes the masculine singular form: ciepły

Compare:

• ciepły wrzesień = a warm September
• jest ciepło = it is warm

So:

• Wrzesień bywa ciepły uses an adjective describing the noun wrzesień
• jest zimno uses an adverb-like predicative form describing the general condition/weather

In Polish, nouns have grammatical gender, and wrzesień is masculine.

You can see that from forms like:

• ten wrzesień = this September
• ciepły wrzesień = warm September

Many month names in Polish are masculine, though not all nouns ending in a consonant are automatically interpreted correctly by learners without practice. Gender is something you usually learn together with the noun.

Wieczorem is a very common Polish way to say in the evening.

It is historically the instrumental case of wieczór (evening), but in modern Polish learners often just memorize it as a fixed time expression:

• rano = in the morning
• wieczorem = in the evening
• nocą = at night

So in this sentence, wieczorem functions adverbially: it tells you when it is already cold.

Normally, no. W wieczór is not the natural choice here.

The idiomatic expression is:

• wieczorem = in the evening

Polish often uses special time expressions instead of a preposition + noun phrase where English would use in.

So for everyday Polish, just learn wieczorem as the standard form.

Because zimno here does not describe a noun. It describes the general situation or weather: it is cold.

Polish commonly uses forms like:

• jest zimno = it is cold
• jest ciepło = it is warm
• jest gorąco = it is hot

These are not adjective forms agreeing with a noun. They are impersonal weather/state expressions.

By contrast, zimny is an adjective and must describe a noun:

• zimny wieczór = a cold evening
• wrzesień jest zimny = September is cold

So:

• Wrzesień bywa ciepły = adjective describing wrzesień
• wieczorem jest już zimno = impersonal expression about the temperature/atmosphere

Because Polish usually does not need a dummy subject like English it in weather expressions.

English says:

• It is cold
• It is warm

Polish simply says:

• Jest zimno
• Jest ciepło

So the English it has no direct equivalent here.

Już usually means already.

In this sentence, it suggests a change or contrast:

• during the day September may still be warm,
• but by evening it is already cold.

So już adds the feeling that the cold comes by that point, perhaps earlier than one might expect, or that the evening cold is now a reality.

Because ale means but, and in Polish it normally introduces a new clause. Clauses joined by ale are separated by a comma.

So:

• Wrzesień bywa ciepły, ale wieczorem jest już zimno.

This is standard punctuation in Polish.

Yes, Polish word order is fairly flexible, though different orders can shift emphasis.

The original sentence is neutral and natural:

• Wrzesień bywa ciepły, ale wieczorem jest już zimno.

You could also say:

• Wrzesień bywa ciepły, ale już wieczorem jest zimno.

This puts a bit more emphasis on already in the evening.

Or:

• Wieczorem jest już zimno, ale wrzesień bywa ciepły.

This changes the information flow and emphasis.

So the original version is a very natural default, but other word orders are possible depending on what you want to highlight.

Yes, it is natural. Bywa is often used when talking about typical but not guaranteed situations.

Examples:

• Lato bywa deszczowe. = Summer can be rainy.
• Październik bywa słoneczny. = October can be sunny.
• Wrzesień bywa ciepły. = September can be warm.

It sounds a bit more nuanced than a simple statement with jest, because it avoids saying that the month is always like that.

It looks difficult mainly because Polish spelling uses several consonant combinations that are unfamiliar to English speakers.

A rough pronunciation guide is:

• wrzesień ≈ VZHE-shyeny / VZHE-shyeń

A few helpful points:

• w sounds like English v
• rz sounds like zh in measure
• ś is a soft sh-like sound
• ń is a soft ny sound

You do not need a perfect English approximation, but recognizing wrzesień as a two-syllable-ish/three-part word with soft consonants helps a lot: wrze-sień.