Learn Hardcore Portuguese (Portugal): Quem quer que toque guitarra na banda tem de saber ler letras em inglês. - Whoever plays guitar in the band has to be able to read lyrics in English.

Quem by itself usually means “who” or “the person who”, e.g. Quem toca guitarra na banda… = The person who plays guitar in the band…
Quem quer que is closer to “whoever / anyone who”, and it adds the idea of any person, no matter who they are.
So:

Quem toca guitarra… = The (specific) person who plays guitar…
Quem quer que toque guitarra… = Whoever plays guitar / Anyone who plays guitar…

Why is it “toque” and not “toca”?

Toque is the subjunctive (conjuntivo) form of tocar (3rd person singular).
Expressions like quem quer que, seja quem for, onde quer que, etc. usually trigger the subjunctive because they talk about an unknown or hypothetical person/situation.
So you use:

Quem toca guitarra… (indicative) when you have a more concrete person in mind.
Quem quer que toque guitarra… (subjunctive) when you mean whoever might play guitar, not a specific known person.

Is “quem quer que” common in spoken European Portuguese, or is it formal?

Quem quer que sounds quite formal and written in European Portuguese.
In everyday speech, people would more often say:

Quem tocar guitarra na banda, tem de saber…
or
Qualquer pessoa que toque guitarra na banda tem de saber…
You will still see quem quer que in writing (rules, formal statements, legal language, etc.).

Why is there no article before “guitarra”? Why not “a guitarra”?

After the verb tocar (to play an instrument), European Portuguese often omits the article when talking in a general sense:

tocar guitarra, tocar piano, tocar violino.
Saying tocar a guitarra is not wrong, but it tends to sound more specific (play the guitar, maybe a particular guitar) or more Brazilian.
In everyday European Portuguese, tocar guitarra (no article) is very natural.

What does “tem de” mean, and how is it different from “tem que”?

Both tem de and tem que can mean “has to / must”.
In Portugal, tem de is more traditional and often preferred, especially in writing. Tem que is also used, especially in spoken language, but some speakers find tem de a bit “cleaner” or more standard.
In Brazil, tem que is much more common in speech.
In European Portuguese, in this sentence, tem de is the most natural choice.

Why is it “tem de saber ler” and not just “tem de ler”?

Saber + infinitive means “know how to (do something)”.
So tem de saber ler letras em inglês means “has to know how to read lyrics in English”, not just “has to read them”.
If you said tem de ler letras em inglês, that would mean they are obliged to read them, but it doesn’t emphasize the skill/ability the way saber ler does.

Does “letras” mean “letters” (like A, B, C) or “lyrics” here?

Letra can mean both “letter (of the alphabet)” and “lyrics”.
In a musical context, letras almost always means song lyrics.
Because this sentence talks about someone who plays guitar in a band, ler letras em inglês is naturally understood as “read lyrics in English”, not alphabet letters.

Is “ler letras em inglês” the normal way to say “read lyrics in English”? Could you just say “ler inglês”?

Yes, ler letras em inglês is a perfectly normal and clear way to say “read lyrics in English”.
You wouldn’t normally say ler inglês for this idea; that just means “read English” in a very general sense (e.g. I can read English = sei ler em inglês).
By including letras, the sentence focuses on song lyrics, not any random English text.

Is the verb “tem” singular because “quem” is grammatically singular, even though it means “whoever (might be)”?

Yes. In Portuguese, quem is grammatically 3rd person singular, so the verb agrees in the singular:

Quem quer que toque guitarra na banda tem de saber…
You do not say “têm de saber” here.
Even though quem can refer to more than one possible person, the grammar still treats it as singular.

What does “na banda” literally mean, and why is it written like that?

Na is the contraction of em + a = “in + the (feminine)”.
So na banda literally means “in the band”.
Contractions like no (em + o), na (em + a), nos (em + os), nas (em + as) are obligatory in standard Portuguese, so you would not normally write em a banda.

Could the word order be changed, or does it have to be exactly “Quem quer que toque guitarra na banda tem de saber…”?

This word order is the normal and natural one.
You could add a comma after the first part:

Quem quer que toque guitarra na banda, tem de saber ler letras em inglês.
Reordering it strongly (e.g. Tem de saber ler letras em inglês quem quer que toque guitarra na banda) is grammatically possible but sounds unusual and stylistically marked, not neutral everyday Portuguese.

How would you say the same idea in a more everyday, less formal way in European Portuguese?

Some more colloquial alternatives in European Portuguese would be:

Quem tocar guitarra na banda tem de saber ler letras em inglês.
Qualquer pessoa que toque guitarra na banda tem de saber ler letras em inglês.
Both sound more natural in speech than quem quer que toque while keeping the same meaning: Anyone who plays guitar in the band has to know how to read lyrics in English.