Bir yandan kamp matını serdik, bir yandan uyku tulumunu açtık.

Here it means while doing one thing, we were also doing another or at the same time.

So the sentence is not really about two opposite ideas. It is describing parallel actions:

• Bir yandan kamp matını serdik
• bir yandan uyku tulumunu açtık

A natural English sense is We spread out the camping mat while also opening the sleeping bag.

Not in this sentence.

Literally, yan means side, so bir yandan can sometimes look like on one side / on the one hand. But in everyday Turkish, the repeated pattern bir yandan ..., bir yandan ... often means meanwhile / at the same time / while also.

So here it is about simultaneous actions, not a contrast between two opinions.

Because Turkish often uses this expression as a paired structure:

• bir yandan X
• bir yandan Y

This shows that X and Y were happening in parallel.

If you only said one bir yandan, the sentence would feel incomplete unless the rest was very clear from context. Repeating it makes the parallel structure obvious.

Those are accusative-marked direct objects.

In Turkish, a direct object often takes the accusative when it is specific/definite. So:

• kamp matını = the/specific camping mat
• uyku tulumunu = the/specific sleeping bag

Compare:

• kamp matı serdik = we spread out a camping mat / camping mat in a less specific sense
• kamp matını serdik = we spread out the / that specific camping mat

The same idea applies to uyku tulumunu.

That n is a very common linking consonant in Turkish.

The nouns kamp matı and uyku tulumu are compounds, and their second words already end in a form that behaves like a possessed/compound ending:

• matı
• tulumu

When a case ending is added after that kind of ending, Turkish normally inserts n:

• kamp matı
  • accusative → kamp matını
• uyku tulumu
  • accusative → uyku tulumunu

So learners often hear this explained as a buffer n.

They are Turkish compound nouns.

Structure:

• kamp matı = camp + mat = camping mat
• uyku tulumu = sleep + bag/sack = sleeping bag

In this kind of compound, the second noun takes a special ending:

• mat → matı
• tulum → tulumu

That is why the basic dictionary-style phrase is not kamp mat or uyku tulum, but kamp matı and uyku tulumu.

They are both simple past, first person plural: we did ...

• serdik = ser-

  • -di
    • -k
  • ser- = spread out, lay out
  • -di = past tense
  • -k = we

• açtık = aç-

  • -tı
    • -k
  • aç- = open
  • -tı = past tense
  • -k = we

Why -di in one and -tı in the other?
Because the past suffix changes according to sound harmony and consonant voicing:

• ser- ends in a voiced sound, so -di
• aç- ends in voiceless ç, so -tı

Because Turkish usually drops subject pronouns when the verb already shows the subject.

Both verbs end in -k, which tells you the subject is we:

• serdik = we spread out
• açtık = we opened

So biz is unnecessary unless you want emphasis:

• Biz bir yandan kamp matını serdik...

That would sound more like we, specifically, did this.

Because the two objects are thought of a little differently.

• sermek is commonly used for spreading/laying out flat things:
  • a rug
  • a blanket
  • a mat

So kamp matını sermek means to spread out / lay out the camping mat.

• açmak literally means to open, but in context it can also mean unfold, unroll, or open up something like a sleeping bag, tent, or folded item.

So uyku tulumunu açtık can mean something like:

• we opened the sleeping bag
• we unrolled/unfolded the sleeping bag

The exact English wording depends on context.

Because Turkish is presenting these as completed past actions in a narrative.

• serdik
• açtık

This is the normal past tense for we did X, we did Y.

Even though the actions happened in parallel, Turkish does not need the progressive to show that, because bir yandan ... bir yandan ... already gives that meaning.

If you used a progressive past form such as seriyorduk or açıyorduk, the focus would shift more toward the ongoing process rather than the completed events.

No, Turkish word order is fairly flexible, but this version is very natural because it highlights the parallel structure:

• Bir yandan kamp matını serdik, bir yandan uyku tulumunu açtık.

The repeated bir yandan at the beginning of each clause makes the pattern clear and balanced.

You may also hear:

• Bir yandan kamp matını serdik, bir yandan da uyku tulumunu açtık.

The da adds a sense of also and is very natural in speech.

So the exact order can change, but the given sentence is a good, idiomatic way to say it.