Známe tuto skutečnost.

Známe is the 1st person plural present tense of znát.

• znát = to know / be familiar with
• znám = I know
• známe = we know

So the sentence has an implied subject: we.

In Czech, subject pronouns are often left out because the verb ending already shows who the subject is.

Here, -me in známe tells you it means we.

So:

• Známe tuto skutečnost. = We know this fact.
• My známe tuto skutečnost. = also possible, but my adds emphasis, like we in we know this fact.

Because tuto skutečnost is the direct object of the verb, so Czech uses the accusative case.

The demonstrative ten / ta / to or tento / tato / toto changes form depending on case and gender.

For feminine singular:

• nominative: tato
• accusative: tuto

So:

• Tato skutečnost je důležitá. = This fact is important.
  Here it is the subject, so nominative.
• Známe tuto skutečnost. = We know this fact.
  Here it is the object, so accusative.

It is in the accusative singular.

Why?

Because znát is a transitive verb and takes a direct object. The thing that is known is the object, so it goes into the accusative.

Here:

• známe = we know
• tuto skutečnost = this fact

So tuto skutečnost is the accusative object.

Good question. In this sentence, only tuto visibly changes, while skutečnost looks the same in nominative and accusative singular.

That is normal for many Czech feminine nouns, especially nouns like skutečnost ending in -ost.

So:

• nominative singular: skutečnost
• accusative singular: skutečnost

The case is still accusative, but the noun form happens to be identical. The demonstrative tuto makes the case especially clear.

The dictionary form is tento.

This demonstrative means this and changes for gender, number, and case.

Some basic nominative forms are:

• tento = masculine
• tato = feminine
• toto = neuter

In your sentence, the noun skutečnost is feminine singular and is in the accusative, so the correct form is tuto.

No. Czech word order is flexible.

Známe tuto skutečnost. is a normal, neutral order.

But you could also say:

• Tuto skutečnost známe.

That puts more attention on tuto skutečnost.

Both are grammatically correct, but the emphasis changes a little. Czech often uses word order to show what is new, important, or contrasted.

Yes. Tu skutečnost is very common and natural.

In everyday Czech, speakers often prefer the shorter form tu instead of tuto.

So both are possible:

• Známe tuto skutečnost.
• Známe tu skutečnost.

The version with tuto can sound a bit more formal, careful, or emphatic.

Not exactly. This is a very common difficulty for English speakers.

znát

Used for being familiar with a person, place, thing, or fact as an object.

Examples:

• Znám Prahu. = I know Prague.
• Znám toho člověka. = I know that person.
• Známe tuto skutečnost. = We know this fact.

vědět

Used more for knowing information, especially with a clause or specific piece of information.

Examples:

• Vím, že je doma. = I know that he is at home.
• Nevím proč. = I don’t know why.

In your sentence, znát works because the object is a noun phrase: tuto skutečnost.

Roughly:

Známe tuto skutečnost
ZNAA-me TOO-to SKOO-tech-nost

A few notes:

• Czech stress is usually on the first syllable of each word.
• á is a long vowel.
• sk in skutečnost is pronounced clearly.
• č sounds like ch in church.

A more approximate pronunciation: [znaa-me too-to skoo-tech-nost]

Skutečnost is a feminine singular noun.

It belongs to a common feminine pattern for nouns ending in -ost. These are often abstract nouns, such as:

• možnost = possibility
• znalost = knowledge
• společnost = society / company
• skutečnost = fact / reality

Because it is feminine, the demonstrative must match it:

• tato skutečnost in nominative
• tuto skutečnost in accusative

Yes, it is grammatical and natural, though it sounds a bit formal or written, especially because of tuto and skutečnost.

In everyday speech, people might often choose slightly simpler wording depending on context, but the sentence itself is completely normal Czech.