Mal sortieren wir Kleidung aus, mal geben wir sie weiter.

Here mal ... mal ... is a fixed pattern meaning sometimes ... sometimes ..., at one time ... at another time ..., or now ... now ....

So:

• Mal sortieren wir Kleidung aus
• mal geben wir sie weiter

means that on some occasions we sort clothes out, and on others we pass them on.

This mal is not the same as the casual particle you hear in sentences like Komm mal her.

German main clauses normally follow the verb-second rule: the finite verb must be in the second position.

In the first clause, mal takes the first position, so the verb sortieren comes next:

• Mal | sortieren | wir | Kleidung | aus

That is why you get Mal sortieren wir ... rather than Mal wir sortieren ....

The same thing happens in the second clause:

• mal | geben | wir | sie | weiter

Because these are separable verbs:

• aussortieren = to sort out
• weitergeben = to pass on

In a main clause, the conjugated part goes in the normal verb position, and the separable prefix moves to the end:

• wir sortieren ... aus
• wir geben ... weiter

This is very common in German:

• anrufen → Ich rufe dich an
• einkaufen → Wir kaufen heute ein
• wegwerfen → Er wirft das weg

Yes. sortieren ... aus here is the split form of aussortieren.

The infinitive is:

• aussortieren

But in a normal main clause it becomes:

• Wir sortieren Kleidung aus

In this context, aussortieren means something like to sort out, to remove from a collection, or to set aside because it is no longer wanted/needed.

Kleidung is usually an uncountable noun, like clothing in English.

So German often uses it without an article when speaking in a general sense:

• Wir sortieren Kleidung aus = We sort out clothing / clothes

You would not normally say Kleidungen here.

You can also use an article in other contexts, for example:

• die Kleidung der Kinder
• meine Kleidung

But in this sentence, the general article-less use is completely natural.

Sie refers back to Kleidung.

Grammatically, Kleidung is a singular feminine noun:

• die Kleidung

So the pronoun is:

• sie

Even though English might think of clothes as plural, German is treating Kleidung as a singular mass noun.

So:

• Kleidung → sie

Because these are two full coordinated clauses, and each clause normally has its own subject:

• Mal sortieren wir Kleidung aus
• mal geben wir sie weiter

Repeating wir makes the structure clear and natural.

In English, we also often repeat the subject in this kind of sentence:

• Sometimes we sort clothes out, sometimes we pass them on

The comma separates two coordinated main clauses:

• Mal sortieren wir Kleidung aus,
• mal geben wir sie weiter.

Each half has its own finite verb and its own subject, so the comma is standard and helpful.

No. It is capitalized only because it is the first word of the sentence.

Normally mal is written with a lowercase m:

• mal ... mal ...

At the beginning of a sentence, it becomes:

• Mal ...

Not really in function.

German mal can come from einmal in some uses, especially in informal speech:

• Komm mal her
• Warte mal

But in mal ... mal ..., it is part of a set expression meaning sometimes ... sometimes .... So it is better to learn this as its own pattern.

Not in exactly the same way.

You could say something like:

• Manchmal sortieren wir Kleidung aus und manchmal geben wir sie weiter.

That is possible, but mal ... mal ... is shorter and more idiomatic for contrasting alternating actions.

So the original version sounds very natural and elegant:

• Mal sortieren wir Kleidung aus, mal geben wir sie weiter.

Weitergeben literally means to give further/on. In this context, it usually means something like:

• to pass on to someone else
• to give away for reuse
• to hand along instead of keeping it

So with clothes, it often suggests donating them, giving them to other people, or otherwise letting someone else use them.

It does not mean simply continue giving here. The idea is passing the clothes on.

It is neutral and natural German.

It would fit well in everyday speech, an interview, an article, or informational writing. It is not slang, and it is not especially formal either.

The mal ... mal ... pattern is common and idiomatic, so it is a useful structure to learn.