Ta pumpička, co je v batohu, nafoukne duši.

Ta is the feminine singular form of the demonstrative pronoun ten / ta / to.

Here it most literally means that:
Ta pumpička = that little pump

In real Czech, though, ten/ta/to is also often used where English would simply say the, especially in speech, when the speaker has a specific thing in mind. So depending on context, ta pumpička can feel like:

• that little pump
• or more loosely the little pump

It agrees with pumpička, which is a feminine noun, so you get ta.

Pumpička is a feminine noun meaning small pump, and it often refers naturally to a bicycle pump or hand pump.

The ending -ička is a diminutive ending, so it can make the word sound:

• smaller
• more specific
• or sometimes just more natural in everyday speech

So:

• pumpa = pump
• pumpička = little pump / small pump

In many contexts, Czech simply prefers pumpička for the kind of portable pump you carry in a bag.

Yes, co often means what, but in everyday Czech it can also introduce a relative clause, especially in speech.

So in this sentence:

co je v batohu = that is in the backpack / which is in the backpack

This is very common colloquial Czech.

More formal or careful Czech would often use která here:

• Ta pumpička, která je v batohu, nafoukne duši.

That means the same thing, but co sounds more conversational and natural in many spoken situations.

Because co je v batohu is a relative clause describing pumpička.

The structure is:

• Ta pumpička = the noun phrase
• co je v batohu = extra information about which pump
• nafoukne duši = main clause

Czech normally separates this kind of clause with commas.

So the comma works much like in English:

• The pump that is in the backpack will inflate the inner tube.

English may omit the comma here, but Czech punctuation rules are stricter about subordinate clauses, so the comma is expected.

Because the preposition v meaning in requires the locative case when it expresses location.

The noun is:

• batoh = backpack

After v, it changes to locative singular:

• v batohu = in the backpack

So this is a case ending issue:

• nominative: batoh
• locative: v batohu

This is a very important Czech grammar point.

Nafoukne is from the verb nafouknout, which is a perfective verb. In Czech, perfective verbs do not normally have a true present meaning. Their present-form endings are used to express the future.

So:

• nafoukne literally looks like a present-form verb
• but it means will inflate / will pump up

Compare:

• fouká = he/she is blowing, blows
• nafoukne = he/she will inflate

So in this sentence:

nafoukne duši = will inflate the inner tube

Duši is the accusative singular of duše.

The verb nafouknout takes a direct object — the thing being inflated — so duše has to go into the accusative.

Declension:

• nominative: duše
• accusative: duši

So:

• duše = inner tube / soul
• nafoukne duši = will inflate the inner tube

This is a regular pattern for many feminine nouns ending in -e.

Yes — duše does also mean soul.

But in practical, everyday contexts, duše can also mean an inner tube, especially for a bicycle tire.

So Czech has two meanings for the same word:

• duše = soul
• duše = inner tube

In this sentence, because we are talking about a pump, the meaning is clearly inner tube.

This kind of vocabulary overlap is very common in languages: the surrounding context tells you which meaning is intended.

It sounds fairly natural and conversational, mainly because of co instead of která.

• Ta pumpička, co je v batohu, nafoukne duši.
  = natural spoken Czech

A slightly more formal or textbook-like version would be:

• Ta pumpička, která je v batohu, nafoukne duši.

Both are correct, but the version with co is more everyday speech.

Yes, Czech word order is flexible, although not completely free.

This sentence has a very normal structure:

• Ta pumpička, co je v batohu, nafoukne duši.

You could also hear variations depending on emphasis, for example:

• Duši nafoukne ta pumpička, co je v batohu.

That puts more focus on duši first.

But the original version is the most neutral and natural if you are simply identifying the pump and saying what it will do.

Not in this sentence.

Here co is acting like a relative pronoun, so co je v batohu means:

• that is in the backpack
• which is in the backpack

If you translated it as what is in the backpack, it would sound like a question or an indefinite thing in English, not a description of pumpička.

So the sentence is not saying:

• That little pump, what is in the backpack...

Instead it means:

• That little pump, which is in the backpack, ...
• or more naturally in English: The little pump in the backpack ...