La noia que treballa a la botiga del barri ven all i pastanagues al taulell.

Yes. In La noia que treballa..., que introduces a relative clause and refers back to la noia.

So:

• la noia = the girl / the young woman
• que treballa a la botiga del barri = who works at the neighborhood shop

Catalan commonly uses que for both who and that in this kind of sentence. English distinguishes more, but Catalan usually does not here.

Catalan normally uses the definite article much more regularly than English.

So La noia is the normal way to say the girl.
Leaving out the article would sound incomplete in this sentence.

This is very common in Catalan:

• La noia... = the girl...
• El noi... = the boy...
• La botiga... = the shop...

Here a means something like at or in, depending on how you translate it naturally into English.

With places, Catalan often uses a where English might use:

• at
• in
• sometimes to, depending on motion

In treballa a la botiga, it means works at/in the shop.

So don't expect a one-to-one match with English prepositions. Catalan a is very flexible.

Because de + el contracts to del in Catalan.

So:

• de + el barri → del barri

This is completely standard.

Here del barri means of the neighborhood or more naturally in the neighborhood / local to the neighborhood, depending on context.
So la botiga del barri is basically the neighborhood shop or the local shop.

Ven is the 3rd person singular present of vendre, meaning to sell.

So:

• jo venc = I sell
• tu vens = you sell
• ell/ella ven = he/she sells

Since the subject is La noia, Catalan uses ven:

• La noia ven... = The girl sells...

Because Catalan often leaves out the article when talking about things in a general, indefinite way.

So:

• ven all i pastanagues = sells garlic and carrots

This sounds natural when referring to products being sold, not to specific garlic and specific carrots already known to the listener.

If you added articles, it could sound more specific depending on context:

• ven l’all i les pastanagues = sells the garlic and the carrots

But in this sentence, the article-free version is the most natural.

Not necessarily. All in Catalan usually works like garlic in English: it is often treated as a mass noun.

So:

• all = garlic
• pastanagues = carrots

This mix is perfectly normal.

If you wanted to talk about individual units, Catalan would usually be more specific, for example:

• un gra d’all = a clove of garlic
• una cabeça d’alls = a head/bulb of garlic

But here all just means garlic in general.

Because a + el contracts to al in Catalan.

So:

• a + el taulell → al taulell

This is parallel to:

• de + el → del

So al taulell means at the counter.

Taulell usually means a counter, especially in a shop, bakery, bar, or similar place.

In this sentence, al taulell means the girl sells the products at the counter.

So it is not a shelf or a table in general; it is specifically the place where goods are displayed or where customers are served.

A useful breakdown is:

• La noia = the girl
• que treballa a la botiga del barri = who works at the neighborhood shop
• ven = sells
• all i pastanagues = garlic and carrots
• al taulell = at the counter

So the main structure is:

• La noia ... ven ...
• The relative clause que treballa... simply gives extra information about la noia.

The core sentence is:

• La noia ven all i pastanagues al taulell.

And then Catalan adds:

• que treballa a la botiga del barri

to identify which girl is being talked about.

The ll in standard Catalan is usually pronounced like a palatal ly sound, roughly similar to the lli sound some English speakers hear in million, though it is not exactly the same.

So:

• all is roughly a-ly
• taulell ends with that same ll sound

A rough guide:

• all ≈ /aʎ/
• taulell ≈ /təwˈʎeʎ/ or a similar regional pronunciation

Depending on the dialect, pronunciation can vary, but learning ll as a ly-type sound is a very good start.