Tato úroveň je vysoká.

Because úroveň is a feminine noun, and the demonstrative this has to agree with it in gender, number, and case.

For this in the singular nominative:

• masculine: ten / tento
• feminine: ta / tato
• neuter: to / toto

So:

• tato úroveň = this level

Using ten or tento here would be grammatically wrong because those are masculine forms.

Czech noun gender is not always obvious from the ending. While many feminine nouns end in -a, some feminine nouns end in a consonant, and úroveň is one of them.

You usually learn the gender together with the noun:

• ta úroveň = the level / that level

A good habit is to memorize new nouns with a matching pronoun:

• ta úroveň
• ten stůl
• to město

That makes gender much easier to remember.

Because the adjective must agree with úroveň.

Here, úroveň is:

• feminine
• singular
• nominative

So the adjective also takes the feminine singular nominative form:

• masculine: vysoký
• feminine: vysoká
• neuter: vysoké

That is why the sentence uses vysoká, not vysoký or vysoké.

It is in the nominative case.

Why? Because tato úroveň is the subject of the sentence:

• This level is high.

After být (to be), the subject stays in the nominative, and the predicate adjective here is also nominative:

• Tato úroveň = nominative
• vysoká = nominative feminine singular

Je is the 3rd person singular form of the verb být (to be).

So:

• je = is

The full structure is:

• Tato úroveň = this level
• je = is
• vysoká = high

So the grammar is very close to English:

• This level is high.

Normally, no in a standard full sentence like this.

Czech does sometimes omit forms of to be in certain styles, such as:

• headlines
• notes
• very informal compressed expressions

But in normal standard speech and writing, you would say:

• Tato úroveň je vysoká.

Leaving out je here would sound incomplete or stylistically unusual.

No. Tato is a standard, neutral form. In everyday speech, people often use tahle.

So you may hear:

• Tato úroveň je vysoká. = standard / neutral
• Tahle úroveň je vysoká. = common spoken Czech

Both are correct.
Tato may sound a bit more careful or formal than tahle.

The sentence as given has a very normal, neutral word order:

• Tato úroveň je vysoká.

Czech word order is more flexible than English, because case endings show grammatical roles. You can change the order for emphasis, but the neutral version is usually best for learners.

For example, a different order might emphasize vysoká:

• Vysoká je tato úroveň.

That is possible, but it is less neutral and more marked. If you are just learning, stick with:

• Tato úroveň je vysoká.

Because Czech has no articles like English a and the.

So Czech simply says:

• Tato úroveň je vysoká.

The meanings that English expresses with a, the, or this are shown in other ways, for example:

• word order
• context
• demonstratives like ten, ta, to, tato, etc.

In this sentence, tato already makes the noun definite and specific: this level.

A rough pronunciation is:

• úroveň ≈ oo-ro-veň

A few useful points:

• ú is a long u
• stress in Czech is usually on the first syllable
• ň is a soft n sound, a bit like the ny sound in canyon, though not exactly the same

So the stress is on Ú:

• Ú-ro-veň

Roughly:

• TA-to Ú-ro-veň ye VY-so-ká

A few notes:

• Czech stress is usually on the first syllable of each word
• je sounds like ye
• á is a long vowel

So:

• Tato → TA-to
• úroveň → Ú-ro-veň
• je → ye
• vysoká → VY-so-ká

The dictionary form is usually the masculine singular nominative:

• vysoký

From that base form, the adjective changes depending on gender, number, and case:

• vysoký = masculine
• vysoká = feminine
• vysoké = neuter / plural in some contexts

So if you look up vysoká in a dictionary, you will normally find it under vysoký.

Not necessarily. Just like English high, Czech vysoký / vysoká / vysoké can be used both literally and more abstractly.

It can describe:

• physical height
• a high level
• a high number
• a high price
• a high standard

So with úroveň (level), vysoká is completely natural.

Yes, it does. Úroveň is a feminine noun and it declines.

Some useful forms are:

• nominative: úroveň
• genitive: úrovně
• dative: úrovni
• accusative: úroveň
• locative: úrovni
• instrumental: úrovní

You do not need to memorize the full table immediately, but it is useful to notice that although the noun ends in a consonant, it still behaves as a feminine noun.