Treballo aquesta part.

Treballo is the 1st person singular present tense form of the verb treballar (to work).

So:

• jo treballo = I work / I am working

In Catalan, verb endings usually show who the subject is, so treballo already tells you the subject is I.

Catalan often omits subject pronouns when they are not needed, because the verb ending already makes the subject clear.

So both are possible:

• Treballo aquesta part.
• Jo treballo aquesta part.

The version without jo is very normal and natural.
You would add jo mainly for emphasis, contrast, or clarity:

• Jo treballo aquesta part, no tu.
  I’m working on this part, not you.

Aquesta means this.

It appears as aquesta because part is a feminine singular noun in Catalan.

The demonstrative must agree with the noun:

• aquest = this, masculine singular
• aquesta = this, feminine singular
• aquests = these, masculine plural
• aquestes = these, feminine plural

Since part is feminine singular, you need:

• aquesta part = this part

Yes. Part is a feminine noun in Catalan.

That is why it takes feminine words with it:

• la part = the part
• aquesta part = this part
• una part = a part

This is something English speakers often need to memorize, since English nouns do not usually have grammatical gender.

Catalan treballar can often be used directly with the thing being worked on, where English may prefer work on.

So Catalan can say:

• Treballo aquesta part.

English may translate that as:

• I work on this part
• I’m working on this part

This is a normal difference between the two languages.
English often needs on, while Catalan may not.

It can potentially cover both ideas, depending on context.

Catalan present tense often corresponds to either:

• I work this part
• I am working on this part

So treballo can express a general present or something happening now.
The surrounding context usually tells you which meaning is intended.

If Catalan speakers want to emphasize an action in progress, they can also use a progressive structure:

• Estic treballant aquesta part.
  I am working on this part.

But the simple present is still very common.

The word order is:

• Treballo = verb
• aquesta part = direct object

So the structure is basically:

• Verb + object

Catalan often allows this kind of sentence without an explicit subject pronoun, so what might look unusual to an English speaker is completely normal:

• Treballo aquesta part.
• literally: Work-I this part

If you include the pronoun, it becomes:

• Jo treballo aquesta part.

A helpful approximate pronunciation is:

• tre-BA-lyo

A few notes:

• The ll in many varieties of Catalan sounds like a y sound.
• The stress is on ba: tre-BA-llo
• The final o is pronounced, unlike in some English words where final vowels may weaken heavily.

Depending on dialect, the exact sound of ll can vary a bit, but for a learner, thinking of treballo as roughly tre-BA-yo is a useful start.

Yes. That would mean more specifically:

• I am working on this part

Compare:

• Treballo aquesta part = I work / I’m working on this part
• Estic treballant aquesta part = more explicitly I am working on this part

So both can be correct, but estic treballant highlights the ongoing action more clearly.

No. The correct form is treballo.

For the verb treballar, the jo form in the present is:

• jo treballo

Not:

• jo treball
• jo treballa

A quick mini-conjugation:

• jo treballo = I work
• tu treballes = you work
• ell/ella treballa = he/she works
• nosaltres treballem = we work
• vosaltres treballeu = you all work
• ells/elles treballen = they work

So in this sentence, treballo is the only correct choice for I.

Yes. Part is a flexible word, much like English part.

Depending on context, aquesta part could mean:

• this part
• this section
• this portion
• this segment

So the sentence could be used in many situations, such as:

• a document
• a task
• a machine
• a performance
• a lesson
• a project

The exact nuance depends on the context already provided.