Learn Hardcore Portuguese (Portugal): A nova edição tem a capa mais bonita de todas, com cores fortes e claras. - The new edition has the most beautiful cover of all, with strong and bright colours.

A nova edição = the new edition, referring to a specific edition that both speaker and listener can identify (for example, the latest edition of a book or magazine).
If you omitted the article and said just Nova edição, it would sound like a title, heading or advertisement slogan, not a normal sentence.

So in a regular sentence, when you mean a specific edition, A is expected.

Could we say nova edição without the article, like English new edition?

Yes, but only in certain contexts:

As a headline or label:
Nova edição já nas bancas! = New edition now in stores!
In lists, menus, catalogues, etc., where you’re not forming a full sentence.

In a full sentence like the one you gave, native speakers would virtually always say A nova edição rather than just Nova edição.

Why is it nova edição and not edição nova? Are both correct?

Both are grammatically correct, but the position of nova slightly changes the nuance.

With many adjectives in Portuguese:

Before the noun: more subjective, usual, or emphasizing a quality.
After the noun: more literal, contrastive, or classifying.

For novo/nova in particular:

nova edição often suggests recent, brand-new:
A nova edição = the latest edition.
edição nova can suggest another/different edition (not necessarily the latest):
Quero uma edição nova = I want a different copy/edition (not the old one I already have).

In your sentence, A nova edição (adjective before noun) is the natural choice to mean the latest edition.

Why is it tem a capa (“has the cover”) instead of something with é (“is”)?

The subject of the sentence is a nova edição, not a capa.

A nova edição tem a capa… = The new edition has the cover…
(You’re saying something about the edition’s cover.)
If you wanted é, you’d change the focus and the subject:
A capa desta edição é a mais bonita de todas.
= The cover of this edition is the prettiest of all.

So with tem, you’re describing a feature that the edition possesses. With é, you’d be making the cover itself the subject.

In a capa mais bonita de todas, why is bonita feminine and todas feminine plural?

Portuguese requires agreement in gender and number:

capa is feminine singular: a capa.
The adjective bonita must agree with capa, so it’s feminine singular: bonita (not bonito).
todas is referring (implicitly) to todas as edições, and edição is feminine, edições is feminine plural. So todas is feminine plural to agree with edições.

So you have:

a capa (fem. sg.)
mais bonita (fem. sg., agreeing with capa)
de todas (as edições) (fem. pl., agreeing with edições, which is understood).

What exactly does de todas mean here? De todas what?

De todas literally means of all (of them).

In full, you could say:

a capa mais bonita de todas as edições
= the prettiest cover of all the editions.

In everyday speech and writing, it’s very common to drop as edições when the context is obvious; the listener knows you’re comparing editions, so de todas is enough.

Is there any difference between a capa mais bonita de todas and a capa mais bonita de todas as edições?

They mean the same thing in this context. The difference is just explicitness:

de todas – shorter, more natural in fluent speech when the context is clear.
de todas as edições – more explicit; you might use it if the reference isn’t obvious, or for extra clarity or formality.

Most of the time, de todas alone sounds perfectly natural.

Could we say a capa mais bonita entre todas instead of de todas?

You can say it, but it’s less idiomatic on its own.

More natural alternatives:

a capa mais bonita de todas (most common)
a capa mais bonita entre todas as edições (ok, but a bit heavier)

Entre tends to be used when you explicitly mention the group:

entre todas as edições
entre todos os livros

So entre todas by itself is not wrong, but de todas is the default, most natural choice here.

Why is there a comma before com cores fortes e claras? Could we omit it?

The comma marks com cores fortes e claras as an additional descriptive detail, almost like an aside:

A nova edição tem a capa mais bonita de todas, com cores fortes e claras.

You could also write it without a comma:

A nova edição tem a capa mais bonita de todas com cores fortes e claras.

Without the comma, it reads more as a single, tightly connected description of the cover. With the comma, com cores fortes e claras feels more like extra information. Both versions are acceptable; the comma here is mostly stylistic.

What does com mean in com cores fortes e claras? Is it just “with”?

Yes, com here corresponds to English with:

com cores fortes e claras = with strong and light colours.

This com is often used in Portuguese to describe attributes or features:

um livro com muitas ilustrações = a book with many illustrations
um carro com ar condicionado = a car with air conditioning

So it’s a normal way to add descriptive detail to the noun (here, a capa).

Why do fortes and claras come after cores? Could they come before?

In Portuguese, adjectives usually come after the noun:

cores fortes
cores claras
um livro interessante

So cores fortes e claras is the normal order.

You could occasionally place certain adjectives before the noun for stylistic effect or a slightly different nuance, but fortes cores claras would sound strange or poetic at best and is not standard in this sentence. Stick to cores fortes e claras.

Do cores fortes and cores claras contradict each other? How can colours be strong and light?

In Portuguese:

cores fortes usually means saturated, vivid, intense colours.
cores claras means light colours, not dark (more white mixed in).

So cores fortes e claras suggests colours that are both:

vivid (not dull or washed-out)
and light (not dark)

Think of bright pastel colours or very vivid, luminous light tones. The two adjectives describe different aspects: intensity and brightness.

What’s the difference between capa and other words like tampa or cobertura for “cover”?

They’re used in different contexts:

capa
- Book, magazine, notebook cover: a capa do livro
- CD/DVD cover, album cover: a capa do álbum
- Sometimes protective outer layer: capa de chuva (raincoat), capa de telemóvel (phone case)
tampa
- Lid or cap of a container: a tampa da garrafa, a tampa da panela.
cobertura
- General covering or coating: cobertura de chocolate (chocolate topping), cobertura de telhas (roofing with tiles).

In your sentence, for the cover of an edition (book, magazine, etc.), capa is the correct and natural word.

Could we say A nova edição tem a mais bonita capa de todas, copying English word order?

No, that word order is unnatural in Portuguese.

You should say:

A nova edição tem a capa mais bonita de todas.

In Portuguese, with expressions like mais … de todas, the adjective phrase comes after the noun:

o livro mais interessante (not o mais interessante livro)
a capa mais bonita (not a mais bonita capa)

Would Brazilians say this sentence differently from Europeans?

The sentence is perfectly natural in both European and Brazilian Portuguese:

A nova edição tem a capa mais bonita de todas, com cores fortes e claras.

Possible minor differences:

Brazilians might be slightly more likely (in some contexts) to say a edição nova instead of a nova edição, but a nova edição is also very common in Brazil.
In speech, a Brazilian might add intensifiers like bem:
…com cores bem fortes e claras.

But grammatically and lexically, your sentence works the same in Portugal and Brazil.