Vytírám kuchyni čisticím prostředkem.

Vytírám is the 1st person singular present tense form of the imperfective verb vytírat.

So it means:

• I am mopping
• I mop
• depending on context, also I’m in the process of wiping/mopping

Because vytírat is imperfective, it is used for an action that is ongoing, repeated, or habitual.

Its perfective partner is vytřít. That verb would be used when you want to express a completed action, for example a future completed result:

• Vytřu kuchyni. = I’ll mop the kitchen / I’ll get the kitchen mopped.

Kuchyni is the accusative singular form of kuchyně (kitchen).

It is in the accusative because it is the direct object of the verb vytírám: it is the thing being mopped.

So the structure is:

• vytírám = I am mopping
• kuchyni = the kitchen

This is a very common Czech pattern: the direct object goes in the accusative case.

In normal usage, vytírat usually refers to mopping or wet-wiping the floor/surface.

So Vytírám kuchyni is naturally understood as:

• I’m mopping the kitchen floor
• not that you are wiping every wall or object in the room

Czech often uses the room name as shorthand, just like English can say I’m mopping the kitchen.

If you want to be completely explicit, you could say:

• Vytírám podlahu v kuchyni. = I’m mopping the floor in the kitchen.

Because Czech often uses the instrumental case to express the means, tool, or substance used to do something.

Here, čisticím prostředkem means:

• with a cleaning agent
• using a cleaning product

Breakdown:

• prostředek = agent, средство/tool/product
• prostředkem = instrumental singular
• čisticí = cleaning
• čisticím = instrumental singular, matching prostředkem

So the instrumental tells you what you are using to mop the kitchen.

Because Czech can express means/instrument with the instrumental alone, without a preposition.

So:

• Vytírám kuchyni čisticím prostředkem.
  naturally means
• I’m mopping the kitchen with a cleaning agent.

If you add s, the meaning can shift toward together with or sound less like the normal bare expression of means.

For tools, materials, and substances, bare instrumental is very common in Czech:

• Píšu perem. = I write with a pen.
• Krájím nožem. = I cut with a knife.

So this sentence follows a very standard pattern.

Čisticí prostředek is a common Czech expression meaning:

• cleaning agent
• cleaner
• cleaning product

Literally:

• čisticí = cleaning
• prostředek = means/agent/product

So it refers to something like a floor cleaner, detergent, or another cleaning substance.

Because adjectives in Czech must agree with the noun they describe in gender, number, and case.

The noun here is:

• prostředkem = instrumental singular of prostředek

So the adjective must also be instrumental singular masculine:

• čisticím prostředkem

This agreement is one of the central features of Czech grammar.

By itself, no.

In this sentence, kuchyni is the direct object in the accusative, so it means the kitchen as the thing being mopped.

To say in the kitchen, you need a preposition:

• v kuchyni = in the kitchen

That is an important distinction:

• Vytírám kuchyni. = I’m mopping the kitchen.
• Vytírám v kuchyni. = I’m mopping in the kitchen.

Even though the form kuchyni can appear after v, the preposition makes the role clear.

Because Czech has no articles.

So kuchyni can mean:

• the kitchen
• a kitchen

and the exact meaning is understood from context.

Likewise, čisticím prostředkem can mean:

• with a cleaning agent
• with the cleaning agent
• with some cleaning product

English requires articles, but Czech usually does not.

No. Czech word order is fairly flexible because the case endings already show the grammatical roles.

The neutral, straightforward order is:

• Vytírám kuchyni čisticím prostředkem.

But other orders are possible for emphasis, contrast, or style, for example:

• Kuchyni vytírám čisticím prostředkem.
• Čisticím prostředkem vytírám kuchyni.

These alternatives do not usually change the basic meaning, but they change what sounds emphasized.

In neutral speech, the given sentence is perfectly natural.