Encara que el microones no és nou, encara funciona molt bé.

Here encara que works as a fixed expression, and together it means although / even though.

So:

• encara on its own = still / yet
• encara que = although / even though

In other words, the first encara is not being used by itself. It is part of the conjunction encara que.

It is repetitive in form, but not strange in Catalan.

The two encara words do different jobs:

• Encara que = although / even though
• encara funciona = still works

So the sentence naturally uses the same word twice, but with two different functions. Catalan speakers would not find that odd.

Good question. After encara que, Catalan can use either the indicative or the subjunctive, depending on meaning.

Here we have no és (indicative) because the speaker is presenting this as a real, known fact: the microwave is not new.

• Encara que el microones no és nou... = the speaker knows it is not new

If the idea were hypothetical, uncertain, or not presented as a fact, Catalan would often use the subjunctive:

• Encara que el microones no sigui nou, el comprarem.
  = Even if the microwave isn’t new, we’ll buy it.

So in your sentence, the indicative fits because the speaker is talking about a real situation.

Because some nouns in Catalan end in -s even in the singular. Microones is one of them.

So:

• el microones = singular
• els microones = plural

The article helps you see the number. Here el tells you it is singular.

This can feel unusual to English speakers, but it is normal. A more explicit form you may also see is forn de microones.

Catalan normally needs an article or another determiner with a singular countable noun. Here el microones means the microwave, referring to a specific one.

So Catalan prefers:

• el microones

rather than leaving the noun bare.

English sometimes drops articles in places where Catalan would not, so this is something learners often have to get used to.

Because adjectives in Catalan usually agree with the noun they describe.

Here:

• microones is masculine singular
• so the adjective is nou = masculine singular

Compare:

• el microones nou = masculine singular
• la nevera nova = feminine singular
• els microones nous = masculine plural
• les neveres noves = feminine plural

So nou matches el microones.

Because bé is an adverb, and it modifies the verb funciona.

• funciona molt bé = it works very well

But bo / bona / bon is an adjective, and adjectives modify nouns:

• És un bon microones = It’s a good microwave

So:

• bé describes how it works
• bo / bon describes what kind of microwave it is

This is similar to English works well vs is good.

The accents help with both meaning and pronunciation.

• és = is
  This is the 3rd person singular of ser
• es without an accent is a different word, usually a pronoun

And:

• bé = well

The accent marks the correct stressed form and helps distinguish the word from other possible spellings. For learners, it is useful to treat these accents as an important part of the word, not as optional extras.

The comma separates the two clauses:

• Encara que el microones no és nou
• encara funciona molt bé

Since the encara que clause comes first, the comma helps show that it is the introductory subordinate clause, followed by the main clause.

This is very similar to English punctuation with a fronted clause:

• Although the microwave isn’t new, it still works very well.

Yes. You could also say:

El microones encara funciona molt bé, encara que no és nou.

That changes the emphasis a bit:

• original sentence: first highlights the contrast
• reordered sentence: first highlights the fact that it still works well

Both are natural. Catalan allows this kind of rearrangement quite easily, especially with subordinate clauses like encara que.