La meva veïna pela una pastanaga i després posa all a la sopa.

Catalan very often uses the definite article before a possessive, so la meva veïna is the normal way to say my neighbor.

Here everything agrees with the noun veïna:

• la = feminine singular article
• meva = feminine singular possessive
• veïna = feminine singular noun

So if the noun changed, the other words would change too:

• el meu veí = my male neighbor
• les meves veïnes = my female neighbors

The ï shows that the i is pronounced in its own syllable. In other words, veïna is pronounced roughly ve-EE-na, not as one blended vowel sound.

This mark is called a diaeresis. It often appears in Catalan to show that two vowels should be pronounced separately.

Also, veïna is the feminine form of veí.

Both are third-person singular present indicative forms:

• pela comes from pelar = to peel
• posa comes from posar = to put, place, add

They match the subject la meva veïna, which is she.

So:

• jo pelo = I peel
• tu peles = you peel
• ella pela = she peels

And similarly:

• jo poso = I put
• ella posa = she puts

Because Catalan often leaves subject pronouns out when they are already clear from the context or the verb form.

Here, once you have La meva veïna, it is understood that the same person is doing both actions:

• pela
• posa

So Catalan does not need to repeat ella.

You could say i després ella posa all a la sopa, but that would usually add emphasis or contrast. Without that special reason, it sounds more natural not to repeat it.

Because pastanaga is being treated as a countable noun, while all is being treated as an ingredient or mass noun.

• una pastanaga = one carrot
• all = garlic in general

In English, this is similar to the difference between:

• a carrot
• garlic

If you want to be more specific about the amount of garlic, Catalan often says:

• un gra d'all = a clove of garlic
• una mica d'all = a little garlic

Because després on its own means afterwards or then.

You use després de only when something comes after it, such as a noun or an infinitive:

• després de dinar = after lunch / after eating
• després de pelar la pastanaga = after peeling the carrot

But if you just mean then or afterwards, després by itself is enough.

With posar, Catalan normally uses a before the place or destination where something is put:

• posar all a la sopa
• posar el llibre a la taula
• posar sucre al cafè

So a la sopa means something like into the soup or in the soup, depending on context.

Also, a + la stays a la. There is no contraction there.
But with masculine singular el, you do get a contraction:

• a + el = al

For example:

• posa sucre al cafè

Yes, a little. Catalan word order is flexible, especially with adverbs like després.

These are all natural:

• La meva veïna pela una pastanaga i després posa all a la sopa.
• Després, la meva veïna posa all a la sopa.
• La meva veïna pela una pastanaga i, després, posa all a la sopa.

The version you have is very normal and straightforward.

You would usually say un gra d'all.

Examples:

• posa un gra d'all a la sopa = she puts a clove of garlic in the soup
• posa dos grans d'all a la sopa = she puts two cloves of garlic in the soup

So:

• all = garlic in general
• un gra d'all = a clove of garlic

Normally, no.

When two verbs share the same subject, Catalan usually states the subject once and then continues with the next verb:

• La meva veïna pela una pastanaga i després posa all a la sopa.

Repeating the subject is possible, but it usually sounds heavier unless you want emphasis, contrast, or extra clarity:

• La meva veïna pela una pastanaga i després la meva veïna posa all a la sopa.

That is grammatical, but not the most natural choice in ordinary speech.