Я предупредил сестру, что на лестнице скользко.

Предупредил is the perfective past form of предупредить, so it presents the warning as a completed single action: I warned my sister.

By contrast, предупреждал is the imperfective past of предупреждать and would usually suggest something like:

• a repeated action,
• an ongoing process,
• or emphasis on the fact of warning rather than the completed result.

So in this sentence, Я предупредил сестру... means I gave her the warning as a completed event.

Also, предупредил shows that the speaker is male. A female speaker would say Я предупредила сестру...

Because предупредить takes a direct object: you warn someone.

So:

• сестра = nominative, dictionary form
• сестру = accusative singular

In this sentence, the sister is the person being warned, so Russian uses the accusative:

• Я предупредил сестру = I warned my sister

This is very common with verbs that act directly on a person or thing.

Что here means that and introduces the content of the warning.

So the structure is:

• Я предупредил сестру = I warned my sister
• что на лестнице скользко = that it was slippery on the stairs/staircase

This is similar to English:

• I warned my sister that it was slippery on the stairs.

Russian often uses что to introduce reported information, statements, or what someone said/warned/explained/knew.

Because на лестнице answers the question where?, not to where?

With на, Russian can use different cases depending on meaning:

• на + prepositional = location, on / in / at
• на + accusative = direction, onto / to

Here the sentence means on the stairs / on the staircase, so it describes a location:

• на лестнице = on the stairs / on the staircase

If you said на лестницу, that would suggest movement onto the staircase, which is not the meaning here.

Because Russian лестница is usually a singular noun meaning:

• staircase
• flight of stairs
• sometimes simply stairs

English often uses the plural stairs, but Russian commonly uses the singular:

• на лестнице = on the stairs / on the staircase

So this is not a strange form; it is just a normal difference between English and Russian.

Скользко is a predicative word meaning it is slippery.

In Russian, words like this are often used in impersonal sentences:

• Здесь холодно = It is cold here
• Мне грустно = I am sad / It is sad for me
• На улице темно = It is dark outside
• На лестнице скользко = It is slippery on the stairs

So скользко does not agree with a subject here, because there is no expressed subject. The sentence is basically impersonal: On the stairs, it is slippery.

Russian often does not use a dummy subject like English it.

English says:

• It is slippery on the stairs

Russian simply says:

• На лестнице скользко

This is a very common pattern. Russian often leaves out an English-style formal subject when talking about weather, conditions, atmosphere, or general states.

Yes. Russian word order is more flexible than English, though the most natural order depends on emphasis.

The original sentence:

• Я предупредил сестру, что на лестнице скользко.

is neutral and natural.

Possible variations include:

• Я предупредил сестру, что скользко на лестнице.
• Сестру я предупредил, что на лестнице скользко.

These alternatives change the focus slightly:

• Сестру я предупредил... emphasizes my sister
• ...что скользко на лестнице may sound slightly more marked or stylistic

For a learner, the original word order is the safest and most standard.

Yes. Предупредить can mean:

• to warn
• to notify beforehand
• to let someone know in advance

The exact nuance depends on context.

In this sentence, because the content is about danger or risk — на лестнице скользко — the natural meaning is warn.

Compare:

• Я предупредил сестру, что опоздаю. = I let my sister know in advance that I would be late.
• Я предупредил сестру, что на лестнице скользко. = I warned my sister that the stairs were slippery.

Yes. It is a subordinate clause introduced by что.

Its structure is a little different from English because Russian often uses impersonal clauses. But it is still a complete idea:

• на лестнице = on the stairs
• скользко = it is slippery

So the whole clause means that it is slippery on the stairs.

Even without an expressed subject, it is still a normal and complete Russian clause.

Yes, because предупредил refers to the time of the warning, not necessarily to whether the stairs are still slippery now.

So the sentence means:

• I warned my sister that it was/is slippery on the stairs

In English, you might choose was or is depending on context. Russian keeps предупредил in the past because the act of warning happened in the past, while the subordinate clause describes the content of that warning.

If the situation is still true now, Russian can still say:

• Я предупредил сестру, что на лестнице скользко.

That is perfectly natural.

Only the past-tense verb form changes:

• Я предупредил сестру... = said by a man
• Я предупредила сестру... = said by a woman

Russian past tense agrees in gender when the subject is singular.

Everything else stays the same:

• Я предупредила сестру, что на лестнице скользко.