Pumpu la aertubon per la pumpilo.

The ending -u is the Esperanto volitive ending. In a sentence like this, it usually gives a command, request, or instruction.

So pumpu means something like:

• pump!
• do the pumping
• please pump

In everyday translation, English usually just uses the imperative: Pump ...

In Esperanto, commands often leave the subject unstated, just like in English.

• Pump the tube.
• Pumpu la aertubon.

The you is understood. If needed, Esperanto can say Vi pumpu, but that is less neutral and usually adds emphasis.

The -n marks the direct object. It shows what is being pumped.

Here:

• pumpu = pump
• la aertubon = the air tube / inner tube

So the sentence is telling you to do the action to the tube, and Esperanto marks that with -n.

Because the two nouns have different jobs in the sentence.

• la aertubon is the direct object, so it gets -n
• per la pumpilo is a prepositional phrase, so pumpilo does not get -n

The word pumpilo is governed by the preposition per, and nouns after ordinary prepositions normally do not take the accusative.

Per means by means of, using, or with the help of.

So per la pumpilo means:

• with the pump
• using the pump
• by means of the pump

It tells you the instrument used to do the action.

Because per is the normal preposition for an instrument or means.

• per la pumpilo = using the pump as a tool

By contrast, kun usually means with, in the sense of together with or accompanied by.

So:

• Mi venis kun mia amiko = I came with my friend
• Mi skribas per krajono = I write with a pencil

A pump is a tool here, so per is the natural choice.

It is built from:

• pump- = the root about pumping
• -il- = tool or instrument
• -o = noun

So pumpilo literally means a tool for pumping.

This is a very common Esperanto pattern. For example:

• tranĉi = to cut
• tranĉilo = a cutting tool, a knife

Esperanto often makes compound words by joining roots together.

Here:

• aero = air
• tubo = tube

Together they form aertubo. In compounds, the earlier part often appears without its final -o, so aero + tubo becomes aertubo.

The last part, tubo, is the main idea, and aer- describes it.

Because there are two separate noun phrases:

• la aertubon
• la pumpilo

Each one can have its own article if both are definite.

So the sentence is talking about:

• the air tube
• the pump

This is normal Esperanto.

Because la is invariable. It never changes form.

So Esperanto says:

• la tubo
• la tubon

Only the noun gets the accusative -n, not the article.

Yes, Esperanto word order is fairly flexible because endings show the grammatical roles.

The given sentence is the most straightforward order:

• Pumpu la aertubon per la pumpilo.

But you could also say:

• Per la pumpilo pumpu la aertubon.

That still means the same thing. The original order is simply the most neutral and easy to follow.

By itself, pumpu does not show singular or plural.

It can mean:

• you, pump!
• you all, pump!

Context tells you which is meant.

If you want to make the subject explicit, you can add it:

• Vi pumpu = you pump
• Vi ĉiuj pumpu = all of you pump
• Ni pumpu = let us pump

So the -u ending gives the command idea, but not the number of the subject.