Poslouchám a přitom tančím.

Yes, you could, but Czech usually leaves out subject pronouns when they are not needed.

Both poslouchám and tančím are 1st person singular forms, so the I is already clear from the verb ending. That is why Poslouchám a přitom tančím sounds natural.

Adding já is possible when you want emphasis or contrast, for example:

Já poslouchám a on jen sedí.
I’m listening, and he is just sitting.

Here přitom means at the same time, meanwhile, or while doing that.

So a přitom tančím is roughly and at the same time I’m dancing.

In other contexts, přitom can sometimes mean something closer to and yet, but in this sentence it clearly expresses simultaneous actions.

Because poslouchat and slyšet are different verbs:

• poslouchat = to listen
  active, intentional
• slyšet = to hear
  passive, just perceiving sound

So if you mean I am listening, poslouchám is the right choice.

Compare:

• Poslouchám hudbu. = I’m listening to music.
• Slyším hudbu. = I hear music.

Czech does not have a separate tense like the English present continuous.

The Czech present tense of an imperfective verb can mean either:

• a general/habitual action: I listen, I dance
• an action happening right now: I am listening, I am dancing

So:

• Poslouchám can mean I listen or I’m listening
• Tančím can mean I dance or I’m dancing

The exact meaning depends on context.

Yes. Poslouchat and tančit are imperfective verbs, and that matters a lot.

Czech uses imperfective verbs for:

• ongoing actions
• repeated actions
• general statements

That is exactly why they are used here: the sentence describes two actions happening at the same time.

A perfective verb in the present tense usually has future meaning instead. For example:

• zatančím = I will dance / I’ll dance, not I am dancing

So tančím is the correct choice for a present ongoing action.

Not necessarily. Czech can leave the object unstated if it is clear from context or simply unimportant.

So Poslouchám a přitom tančím can stand on its own, just like English I’m listening and dancing at the same time.

If you want to say what you are listening to, you can add it:

• Poslouchám hudbu a přitom tančím. = I’m listening to music and dancing at the same time.
• Poslouchám tě a přitom tančím. = I’m listening to you and dancing at the same time.

Tančím is the 1st person singular present form of tančit.

So:

• infinitive: tančit = to dance
• tančím = I dance / I’m dancing

Many Czech verbs ending in -it form I with -ím, so this pattern is very common.

Similarly:

• prosit → prosím
• vidět → vidím
• tančit → tančím

Yes, you could. Czech word order is more flexible than English word order.

The original sentence, Poslouchám a přitom tančím, is a natural neutral version.
If you say Tančím a přitom poslouchám, the meaning stays basically the same, but the focus shifts slightly toward tančím.

So both are correct:

• Poslouchám a přitom tančím.
• Tančím a přitom poslouchám.

Czech often uses word order to highlight what feels more important or more topical.

No, normally not in this sentence.

A is the conjunction and, joining two coordinated parts, and přitom does not force a comma here.

So the normal punctuation is:

Poslouchám a přitom tančím.

A rough guide:

PO-slou-chám a PŘI-tom TAN-čím

A few important points:

• Czech stress is usually on the first syllable of each word.
• á and í are long vowels.
• ou in poslouchám is a diphthong, somewhat like oh + oo blended together.
• ch in poslouchám is not English ch. It sounds like the ch in Scottish loch or German Bach.
• č in tančím sounds like English ch in church.
• ř in přitom is the famous Czech sound. It is difficult for learners; an approximate beginner version is something like rzh, but the real sound is uniquely Czech.

So a very rough English-friendly approximation might be:

PO-sloh-khaam a PRZHI-tom TAN-cheem

but that is only approximate.