Ten tunel pod rzeką jest długi, ale prowadzi prosto do centrum.

No. Polish does not have articles like the or a/an.

Ten is a demonstrative word, meaning this or sometimes that, depending on context. In this sentence, ten tunel means this tunnel.

So:

• ten tunel = this tunnel
• not simply the tunnel

Because tunel is a masculine singular noun.

In Polish, demonstratives have to agree with the noun in gender, number, and case:

• ten = masculine singular
• ta = feminine singular
• to = neuter singular

Since tunel is masculine, the correct form is ten tunel.

A very common pattern in Polish is:

• nouns ending in a consonant are often masculine
• nouns ending in -a are often feminine
• nouns ending in -o, -e, or -um are often neuter

Tunel ends in a consonant, so it is masculine.

You can also see this from agreement:

• ten tunel
• tunel jest długi

Both ten and długi are masculine forms, confirming that tunel is masculine.

Because the preposition pod can take different cases depending on the meaning.

Here it means location: the tunnel is under the river. With a static location, pod takes the instrumental case.

So:

• pod rzeką = under the river / beneath the river

If you were talking about movement toward a position under something, you would use the accusative:

• pod rzekę would only make sense in a movement-type pattern, but with river it is not a normal phrase in this context

So in this sentence, pod rzeką is correct because it describes where the tunnel is.

Rzeką is the instrumental singular form of rzeka.

For many feminine nouns ending in -a, the instrumental singular ends in -ą:

• rzeka → rzeką
• ulica → ulicą
• książka → książką

So the ending -ą here tells you that the noun is in the instrumental case.

Because adjectives in Polish must agree with the noun they describe.

The noun tunel is:

• masculine
• singular
• nominative

So the adjective must also be masculine singular nominative:

• długi = long for a masculine singular noun

Compare:

• długi tunel = a long tunnel
• długa rzeka = a long river
• długie okno = a long/big window shape-wise, neuter form

In this sentence, jest długi means is long.

Yes, in normal standard Polish, you do.

Jest is the 3rd person singular of być (to be), and here it links the subject to the adjective:

• Ten tunel ... jest długi = This tunnel ... is long

Unlike Russian, Polish normally keeps to be in the present tense in sentences like this.

So:

• correct: Tunel jest długi
• not standard as a full normal sentence: Tunel długi

Because Polish often leaves out a repeated subject when it is already clear.

In English, you would usually repeat it:

• This tunnel ... is long, but it leads ...

In Polish, after ten tunel has already been introduced, the second clause can simply use the verb:

• ... ale prowadzi prosto do centrum

The subject is still understood to be ten tunel.

This is very natural in Polish.

Here prowadzi means leads.

It comes from prowadzić, which often means:

• to lead
• to guide
• to conduct
• to run or to go to, for roads, paths, tunnels, stairs, etc.

So in this sentence, the tunnel is being described as something that leads straight to the center.

This use is very common with things like:

• droga prowadzi do wsi = the road leads to the village
• schody prowadzą na górę = the stairs lead upstairs

Prosto here means straight or directly.

It is an adverb, so it modifies the verb prowadzi:

• prowadzi prosto do centrum = leads straight/directly to the center

It suggests a direct route, without turns or detours.

The preposition do requires the genitive case.

So do centrum means to the center or into the center.

The reason centrum looks unchanged is that this noun often has the same form in the singular after several prepositions and in several cases.

So although the case after do is genitive, the form is still:

• centrum

That is why you get:

• do centrum
• w centrum

even though the grammatical cases are different.

Yes, Polish word order is fairly flexible, but changing it changes the emphasis or style.

The given sentence is natural:

• Ten tunel pod rzeką jest długi, ale prowadzi prosto do centrum.

It presents the tunnel first, then describes it.

You could also say:

• Ten tunel jest długi, ale prowadzi prosto do centrum.

That still works, but it no longer includes pod rzeką.

If you move pod rzeką around, the sentence may sound more marked or literary, and the focus may shift.

So the original order is a very normal, neutral way to say it.