Ten proces trwa długo.

Because proces is a masculine singular noun in the nominative case, and the demonstrative must agree with it.

Polish this changes form depending on gender:

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

So:

• ten proces = this process
• not ta proces
• not to proces

In Polish, many nouns ending in a consonant are masculine, and proces ends in -s.

So learners will usually recognize proces as a masculine noun. In this sentence, it is also the subject, so it appears in the nominative singular form: proces.

Here ten means this.

It points to a specific process that the speaker has in mind: this process.

A useful comparison:

• ten proces = this process
• tamten proces = that process

In real use, ten can sometimes feel close to English this or just a way of specifying the one we’re talking about.

Trwa is the 3rd person singular present tense form of the verb trwać.

So:

• trwać = to last, to continue
• trwa = lasts / is lasting / continues

It matches the subject ten proces, which is singular.

A few related forms:

• proces trwa = the process lasts
• procesy trwają = the processes last

Because Polish normally uses trwać when talking about something lasting in time.

English often says:

• The process takes a long time
• The process lasts a long time

Polish naturally says:

• Proces trwa długo

Using być (to be) here would not express duration correctly. So trwać is the normal verb for this idea.

Długo is an adverb, not an adjective.

It means for a long time or long in the sense of duration.

Compare:

• długi proces = a long process
  
  • here długi is an adjective
• proces trwa długo = the process lasts a long time
  
  • here długo is an adverb

So in your sentence, długo describes the verb trwa, not the noun proces.

Because Polish does not have articles like English a and the.

Whether something is a process, the process, or this process is understood from context or from words like ten.

So:

• proces can mean a process or the process
• ten proces makes it more specific: this process

Not completely. Ten proces trwa długo is a very natural, neutral word order.

But Polish word order is more flexible than English, so you can move things around for emphasis:

• Ten proces trwa długo. = neutral
• Długo trwa ten proces. = emphasis on how long
• Ten długo trwa proces. = not natural in normal speech

So the original sentence is the safest and most standard version for learners.

Yes. Proces ten trwa długo is grammatically correct.

It means the same thing, but it sounds a bit more formal, written, or stylistically marked than Ten proces trwa długo.

For everyday neutral speech, Ten proces trwa długo is usually the better choice.

A simple learner-friendly guide:

• ten ≈ ten
• proces ≈ PRO-tsess
• trwa ≈ trvah
• długo ≈ DWOO-go

A couple of important pronunciation points:

• Polish w sounds like English v
• Polish ł sounds like English w
• So dł in długo sounds roughly like dw
• In proces, the letter c sounds like ts

Stress in Polish is usually on the second-to-last syllable:

• PRO-ces
• DŁU-go

By itself, długo is usually neutral. It just means for a long time.

So:

• Ten proces trwa długo. = This process takes a long time / lasts a long time.

If you want to say too long, Polish commonly uses:

• Ten proces trwa za długo. = This process takes too long.

So długo is neutral, while za długo is clearly negative.

It is in the nominative case, because it is the subject of the sentence.

The basic structure is:

• Ten proces = subject
• trwa = verb
• długo = adverb

So nothing unusual is happening with case in this sentence: it is just a straightforward subject + verb + adverb sentence.

You change the verb trwać.

Present:

• Ten proces trwa długo. = This process lasts a long time.

Past:

• Ten proces trwał długo. = This process lasted a long time.

Future:

• Ten proces będzie długo trwał. = This process will last a long time.

Because proces is masculine singular, the past form is trwał.

Trwać is an imperfective verb.

That makes sense, because duration is naturally connected with an ongoing or extended action/state. In this sentence, we are talking about how long the process continues, so the imperfective verb is exactly what Polish wants here.

For a learner, the important practical point is:

• trwać = the normal verb for to last / to continue over time
• trwa = the present-tense form used in this sentence