Vi povas uzi vifion, kondiĉe ke la modemo funkcias.

Because vifion is the direct object of uzi (to use), so it takes the accusative ending -n.

• vifio = Wi-Fi
• vifion = Wi-Fi as the thing being used

In Esperanto, the thing directly affected by the verb usually gets -n.

Compare:

• Mi uzas la komputilon. = I use the computer.
• Vi povas uzi vifion. = You can use Wi-Fi.

After povi (can / to be able to), Esperanto uses the infinitive form of the next verb.

So:

• povas uzi = can use
• not povas uzas

This is similar to English:

• You can use
• not You can uses

A few examples:

• Mi povas veni. = I can come.
• Ŝi povas helpi. = She can help.

Kondiĉe ke means provided that, on condition that, or as long as.

It introduces a condition that must be true.

So:

• Vi povas uzi vifion, kondiĉe ke la modemo funkcias. means:
• You can use the Wi-Fi, provided that the modem is working.

It is a set phrase, so it is best learned as one unit:

• kondiĉe ke = provided that

Because ke introduces the subordinate clause, like that in English.

In this sentence:

• kondiĉe ke la modemo funkcias

the part after ke is the condition: the modem works / is working.

Many Esperanto learners just memorize the full expression:

• kondiĉe ke = provided that

You usually would not separate it in your mind at first.

Funkcias means works / is functioning.

So:

• la modemo funkcias = the modem is working

This is the normal intransitive verb for something operating correctly.

By contrast, funkciigi means to make something function or to operate something.

So:

• La modemo funkcias. = The modem works.
• Li funkciigas la maŝinon. = He operates the machine / makes the machine run.

In your sentence, the modem itself is the thing functioning, so funkcias is correct.

Because la modemo is the subject of funkcias, not the object.

In the clause:

• la modemo funkcias

la modemo is the thing doing the action of functioning.

Esperanto marks:

• direct objects with -n
• subjects with no -n

So:

• Vi povas uzi vifion → vifion gets -n because it is the object
• la modemo funkcias → la modemo has no -n because it is the subject

Vi can mean:

• you singular
• you plural
• formal you

Esperanto uses vi for all of these, unlike languages that make a distinction between informal singular and plural/formal forms.

So this sentence could mean:

• You can use the Wi-Fi...
• You all can use the Wi-Fi... depending on context.

La means the, so la modemo means the modem.

Using la suggests a specific modem, probably one already known from context, such as the modem in a house, office, or café.

Without la, modemo would sound more general or less specific.

So:

• la modemo = the modem
• modemo = a modem / modem in a more general sense

In this sentence, a specific modem is meant, so la modemo is natural.

Yes, vifio is an Esperanto-style adaptation of Wi-Fi.

Esperanto often adapts international or technical words to Esperanto spelling and word structure. That is why you see:

• vifio
• modemo

Learners may also sometimes encounter Wi-Fi written in its original form, especially in informal or technical contexts, but vifio fits Esperanto spelling better.

In this sentence:

• vifio is the noun
• vifion is its accusative form

It is pronounced roughly like:

• vee-FEE-on

Breaking it down:

• vi = vee
• fi = fee
• on = on

Remember that Esperanto pronunciation is regular, and each vowel is pronounced clearly.

So vifion has three syllables:

• vi-fi-on

A rough English approximation is:

• FOONK-tsee-as

Broken into parts:

• funk = roughly foonk
• ci = tsee
• as = ahs

So:

• funk-ci-as

A useful thing to remember is that Esperanto c sounds like ts, so funkcias is not pronounced like English funkias.

Esperanto present tense often covers both simple present and present progressive meanings.

So:

• funkcias can mean works
• or is working

The exact meaning comes from context.

That is very common in Esperanto:

• Mi legas. = I read / I am reading
• La modemo funkcias. = The modem works / The modem is working

So funkcias is completely normal here.

Yes. Because povas can correspond to can, may, or be able to, depending on context.

And kondiĉe ke can mean:

• provided that
• on condition that
• as long as

So several English translations are possible, such as:

• You can use the Wi-Fi, provided that the modem is working.
• You may use the Wi-Fi as long as the modem works.
• You are able to use the Wi-Fi, provided that the modem functions.

The Esperanto grammar stays the same; only the English wording shifts a little.

Yes, Esperanto word order is fairly flexible, though some orders sound more natural than others.

The original:

• Vi povas uzi vifion, kondiĉe ke la modemo funkcias.

is clear and natural.

You could also say:

• Kondiĉe ke la modemo funkcias, vi povas uzi vifion.

This puts the condition first:

• Provided that the modem is working, you can use the Wi-Fi.

Because Esperanto uses endings like -n to mark grammar, word order is often freer than in English. Still, the most neutral order is usually the easiest for learners.