Al vespre, faig els deures al meu quadern amb un llapis.

Because al is the contraction of a + el.

• vespre is a masculine noun: el vespre
• so a el vespre becomes al vespre

As a time expression, al vespre means in the evening. Catalan often uses this pattern with parts of the day, for example:

• al matí = in the morning
• a la tarda = in the afternoon
• a la nit = at night

Not exactly.

• vespre = evening
• nit = night

So al vespre refers to the earlier part of the evening, while a la nit refers to nighttime more generally.

Catalan often leaves out subject pronouns because the verb ending already tells you who the subject is.

Here, faig already means I do, so jo is not necessary.

You would add jo only for emphasis or contrast, for example:

• Jo faig els deures, però ell no.
  = I do my homework, but he doesn’t.

Faig is the first-person singular present tense of fer, which means to do or to make.

So:

• fer = to do / to make
• faig = I do / I make

This verb is irregular. The present tense is:

• faig = I do
• fas = you do
• fa = he/she/it does
• fem = we do
• feu = you all do
• fan = they do

Because in Catalan, the normal expression is fer els deures.

English says do homework without an article, but Catalan usually uses the definite article here:

• els deures = homework

Also, deures is usually plural in this meaning. A single deure is more like a duty, an obligation, or sometimes one assignment/exercise, depending on context.

Catalan usually treats homework as a plural idea: els deures.

So even though English uses the uncountable noun homework, Catalan normally uses the plural noun deures. That is just the standard idiomatic way to say it.

Because Catalan normally uses the definite article before possessives.

So you usually get:

• el meu quadern = my notebook
• la meva casa = my house
• els meus llibres = my books

Here, al meu quadern comes from a + el meu quadern.

Also, meu agrees with quadern, not with the owner:

• quadern is masculine singular
• so the possessive is meu

Here al again is a + el.

Catalan a can correspond to several English prepositions depending on context, including to, at, in, or on. In this sentence, al meu quadern means something like in my notebook or on my notebook/workbook, depending on the exact situation.

So:

• el meu quadern = my notebook
• al meu quadern = in/on my notebook

Sometimes yes, depending on context and style.

Both a and en can be used for location in Catalan, and actual usage varies by speaker and region. In everyday Catalan, al meu quadern sounds very natural. En el meu quadern can also be possible, especially if you want to emphasize being inside the notebook.

So the original sentence is perfectly normal, and it is a good pattern to learn.

Because Catalan normally uses the indefinite article here:

• amb un llapis = with a pencil

This is the natural way to mention the tool or instrument you are using. Leaving out un would sound less natural in a normal full sentence.

Not completely. Catalan word order is fairly flexible, but this sentence has a very natural, neutral order:

• Al vespre = time
• faig = verb
• els deures = object
• al meu quadern = place/location
• amb un llapis = instrument

You could also say:

• Faig els deures al vespre al meu quadern amb un llapis.
• Al vespre faig els deures al meu quadern amb un llapis.

The original version sounds smooth and natural, and the comma after Al vespre helps separate the opening time phrase.