У курицы было мокрое перо на хвосте, потому что утром шёл дождь.

Russian often expresses possession with у + genitive plus a form of быть.

So У курицы было мокрое перо literally means something like By the chicken there was a wet feather, but in natural English that becomes The chicken had a wet feather.

Here:

• курица = chicken
• у курицы = by the chicken / in the chicken’s possession

After у, the noun goes into the genitive case, so курица becomes курицы.

Russian has no articles, so there is no direct equivalent of a or the.

That means курицы could refer to:

• a chicken
• the chicken
• sometimes even the hen, depending on context

You decide from the situation, the previous sentence, or the translation you have been given.

Because было agrees with перо, not with курицы.

The noun перо is:

• neuter
• singular

So the past tense of быть here is было.

This is a very common pattern in Russian possession/existence sentences:

• У меня был брат. = I had a brother.
• У меня была сестра. = I had a sister.
• У меня было письмо. = I had a letter.

The verb matches the thing that existed or was possessed, not the owner.

Because the adjective must agree with the noun in:

• gender
• number
• case

Перо is:

• neuter
• singular
• nominative

So мокрый becomes мокрое.

Compare:

• мокрый хвост = a wet tail
• мокрая курица = a wet chicken
• мокрое перо = a wet feather
• мокрые перья = wet feathers

Yes, taken literally, перо means a feather, so the sentence says there was one wet feather on the tail.

If you wanted to say wet feathers, you would normally use the plural:

• мокрые перья

Russian sometimes uses singular nouns where English might prefer plural, but in this sentence the most straightforward reading is really one feather.

Because this sentence describes location, not motion.

With на:

• на + prepositional usually means on / at a place
• на + accusative often means movement onto something

So:

• на хвосте = on the tail
• на хвост would suggest movement onto the tail

Here the feather is already located there, so на хвосте is correct.

Хвосте is the prepositional case singular of хвост.

The preposition на takes the prepositional case when it means on in a static location:

• на столе = on the table
• на крыше = on the roof
• на хвосте = on the tail

So:

• dictionary form: хвост
• prepositional singular: хвосте

Russian often leaves out possessive words like his, her, or its when the owner is obvious from context, especially with body parts or parts of an animal.

So на хвосте naturally means on its tail here, because the sentence is already about the chicken.

You could say на её хвосте, but it would sound more explicit and is often unnecessary.

Утром is the instrumental case of утро, used adverbially to mean in the morning.

Russian often uses the instrumental this way with parts of the day:

• утром = in the morning
• днём = in the daytime
• вечером = in the evening
• ночью = at night

So утром шёл дождь means it rained in the morning or more literally rain was falling in the morning.

Yes, шёл is the masculine past tense of идти, but Russian uses идти idiomatically for weather such as rain and snow.

So:

• идёт дождь = it is raining
• шёл дождь = it was raining / rain was falling
• идёт снег = it is snowing

The form шёл is masculine because дождь is a masculine noun.

This is just a normal Russian weather expression, even though it sounds strange if translated word for word as rain was going.

Because потому что introduces a subordinate clause giving the reason.

Main clause:

• У курицы было мокрое перо на хвосте

Reason clause:

• потому что утром шёл дождь

Russian punctuation normally separates these with a comma:

• ..., потому что ...

This is similar to English:

• ..., because ...

Yes. Russian word order is fairly flexible, and changing it usually changes emphasis, not the basic meaning.

For example:

• У курицы было мокрое перо на хвосте... = neutral
• На хвосте у курицы было мокрое перо... = emphasizes the location
• Утром шёл дождь, поэтому у курицы было мокрое перо на хвосте. = starts with the cause

The version you have is a natural, straightforward way to say it.