Depois fui à papelaria comprar um caderno novo e papel para a impressora.

Fui is the 1st person singular preterite of ir (to go). So it means I went.

This tense is used for a completed action in the past:

• fui = I went
• foste = you went
• foi = he/she/it went

It is irregular, so it has to be learned as a special form.

À is a contraction of:

• a = the preposition to
• a = the feminine definite article the

So:

• a + a papelaria = à papelaria

This happens because papelaria is feminine, and with ir in European Portuguese, the destination is often introduced by a.

Compare:

• fui à papelaria = I went to the stationery shop
• fui ao supermercado = I went to the supermarket

The accent in à marks the contraction. It is not the same as á or a.

À papelaria suggests the stationery shop: a specific one, or one that is clear from the context.

A uma papelaria would mean to a stationery shop, with a less specific meaning.

So the sentence sounds like the speaker has a particular shop in mind, even if English might sometimes just say to a stationery shop or to the stationer’s depending on context.

Because after ir, standard European Portuguese normally uses a or sometimes para for destination, not em.

So:

• fui à papelaria = correct
• fui para a papelaria = also possible
• fui na papelaria = not standard in European Portuguese

But na papelaria is correct with verbs of location or entry, for example:

• estou na papelaria = I am in the stationery shop
• entrei na papelaria = I went into the stationery shop

Because it expresses purpose: what the speaker went there to do.

So:

• fui à papelaria comprar... = I went to the stationery shop to buy...

This is a very common Portuguese structure:

• Fui ao supermercado comprar fruta.
• Sai de casa buscar pão.

After a verb of movement, Portuguese often uses a plain infinitive like this to show purpose.

Yes. Fui à papelaria para comprar... is grammatically correct.

However, fui à papelaria comprar... is usually more natural and direct in this kind of sentence. After verbs of movement, Portuguese very often leaves out para.

So:

• fui à papelaria comprar... = very natural
• fui à papelaria para comprar... = also correct, slightly more explicit

In Portuguese, adjectives often come after the noun, so caderno novo is the normal, straightforward order.

• um caderno novo = a new notebook

If you put novo before the noun, it can sound more literary, emphatic, or sometimes slightly change the nuance. In many contexts, novo caderno may suggest another notebook or give a more marked style.

For a simple neutral meaning, um caderno novo is the best choice.

Because caderno is a countable noun, while papel here is being used as an uncountable material noun.

• um caderno = one notebook
• papel = paper in general / some paper

In Portuguese, singular countable nouns normally need a determiner:

• um caderno
• o caderno
• este caderno

But with uncountable nouns, no article is often possible when speaking generally:

• comprei papel
• preciso de água
• há pão em casa

If you mean a sheet of paper, you would say:

• uma folha de papel

Papel para a impressora means paper for the printer, in other words printer paper.

Yes, papel de impressora is also possible. The difference is mostly one of nuance:

• papel para a impressora emphasizes purpose/use: paper to use in the printer
• papel de impressora is a more compact label-like expression: printer paper

In everyday speech, papel para a impressora sounds very natural.

Portuguese uses definite articles more often than English does. Here, a impressora sounds natural because it refers to a specific printer that is understood from the context, such as the one at home or at the office.

So:

• papel para a impressora = paper for the printer

Without the article, the phrase would sound less natural in this sentence.

Here Depois means afterwards, then, or later. It helps move the story forward.

• Depois fui à papelaria... = Then I went to the stationery shop...

Yes, it can move, but the beginning of the sentence is very common in narration.

Also, a useful distinction:

• depois = afterwards / then
• depois de = after

For example:

• Depois fui para casa. = Afterwards I went home.
• Depois de jantar, fui para casa. = After dinner, I went home.

Usually yes: caderno means a notebook or exercise book made of paper pages.

A useful warning for English speakers: it does not mean a laptop computer. In Portugal, a laptop is usually:

• um portátil
• um computador portátil

So in this sentence, um caderno novo is definitely a paper notebook, not an electronic device.