На крыльце было мокро после дождя, но кошка всё равно ждала у двери.

Because крыльцо means porch / front steps / stoop, and in Russian you normally say на крыльце = on the porch.

• на is used for being on a surface / area
• в would mean in(side) something

So:

• на крыльце = on the porch
• в доме = in the house

Here крыльце is in the prepositional case after на:

• крыльцо → на крыльце

Было мокро is a very common impersonal way to say it was wet or things were wet there.

Russian often uses this pattern to describe conditions:

• было холодно = it was cold
• было темно = it was dark
• было шумно = it was noisy
• было мокро = it was wet

So На крыльце было мокро literally feels like:

• On the porch, it was wet

If you said крыльцо было мокрое, that would mean the porch was wet, focusing more directly on the porch as a noun. Both are possible in some contexts, but на крыльце было мокро sounds very natural when describing the overall situation or conditions.

Here мокро is a predicative word (sometimes treated as a special adverb-like form used in impersonal sentences).

It does not agree with a noun the way a normal adjective would:

• мокрый пол = a wet floor
• мокрая кошка = a wet cat
• мокро = wet (as a condition)

So in было мокро, мокро describes the state of the environment, not a noun directly.

Because после requires the genitive case.

• dictionary form: дождь = rain
• genitive singular: дождя

So:

• после дождя = after the rain

This is a very useful pattern to remember:

• после урока = after the lesson
• после работы = after work
• после фильма = after the movie

Yes, но here means but and contrasts the two parts of the sentence:

• На крыльце было мокро после дождя = It was wet on the porch after the rain
• но кошка всё равно ждала у двери = but the cat was still waiting by the door

So the contrast is:

• the porch was wet
• despite that, the cat kept waiting

Here всё равно means all the same, anyway, or still.

It shows that something happened despite the circumstances.

So:

• но кошка всё равно ждала = but the cat waited anyway / still waited

Very common uses:

• Я устал, но всё равно пойду. = I’m tired, but I’ll go anyway.
• Было холодно, но они всё равно гуляли. = It was cold, but they walked anyway.

Important: in this sentence, всё равно does not mean it’s all the same / I don’t care. Here it means despite that.

Ждала is the past tense, feminine singular form of ждать (to wait).

Russian past tense agrees with gender and number:

• ждал = he waited
• ждала = she waited
• ждало = it waited
• ждали = they waited

Since кошка is a feminine noun, the verb is feminine too:

• кошка ждала = the cat waited / was waiting

In Russian, the past tense of an imperfective verb often covers both:

• waited
• was waiting

So ждала can mean either depending on context.

Because ждать is imperfective, it fits an ongoing situation well:

• the cat was in the state of waiting
• the action is not presented as a completed event

That is exactly what you would want here.

У двери means by the door / next to the door / at the door. It is a very natural and common expression.

• у
  • genitive often means near / by
• двери is genitive singular of дверь

Other options are possible, but they are slightly different:

• у двери = by the door, at the door
• около двери = near the door
• перед дверью = in front of the door

Here у двери is probably the most natural choice for a waiting cat.

Because у requires the genitive case.

• dictionary form: дверь
• genitive singular: двери

So:

• у двери = by the door

This is a common pattern:

• у окна = by the window
• у дома = by the house
• у стола = by the table

Yes, Russian word order is flexible, but the given order sounds natural and clear.

Current sentence:

• На крыльце было мокро после дождя, но кошка всё равно ждала у двери.

Why this order works:

• it first sets the scene: On the porch, it was wet after the rain
• then gives the contrast: but the cat was still waiting by the door

You could rearrange parts, for example:

• После дождя на крыльце было мокро, но кошка всё равно ждала у двери.

That puts more emphasis on after the rain first. Both are natural.

It could mean either the cat or a cat, because Russian has no articles.

So кошка can mean:

• the cat
• a cat

You figure it out from context. In this sentence, English might naturally choose the cat if the cat is already known in the story, but Russian itself does not mark that distinction.

Because Russian often uses impersonal sentences without a subject where English uses it.

English says:

• It was wet
• It was cold
• It was dark

Russian often just says:

• Было мокро
• Было холодно
• Было темно

So the English dummy it usually has no direct Russian equivalent.

Yes. Russian allows that phrase to move fairly freely.

For example:

• После дождя на крыльце было мокро, но кошка всё равно ждала у двери.
• На крыльце после дождя было мокро, но кошка всё равно ждала у двери.

These all mean roughly the same thing, but the emphasis changes slightly.

• После дождя... puts time/background first
• На крыльце... puts location first

The original sentence is completely natural.