kono kafe nara, muryou no waifai ni setuzoku dekiru.

Here, なら gives a meaning like if it’s this café or as for this café.

So このカフェなら suggests:

• this café is being picked out from other possible places
• there may be some contrast, such as other places might not have Wi‑Fi, but this one does

It is not just a plain location marker. It has a nuance like:

• If we’re talking about this café, you can connect
• At least in this café, you can connect

この must be followed by a noun, so:

• このカフェ = this café

ここ means here and stands on its own.

So:

• このカフェなら = if it’s this café / as for this café
• ここなら = if it’s here / here, then

Both can be natural in the right context, but they focus slightly differently:

• このカフェ points to the café as a place or establishment
• ここ points more directly to the location

無料 means free of charge, but before a noun it commonly links with の:

• 無料のワイファイ = free Wi‑Fi
• 無料の駐車場 = free parking lot

So the の connects 無料 to the noun that follows.

A learner may expect な, but 無料なワイファイ is not the normal form here. 無料の is the natural pattern.

Also, in signs or ads, you may often see:

• 無料Wi‑Fi

This is a more compressed written style.

接続できる is the potential form meaning can connect or be able to connect.

It comes from:

• 接続する = to connect
• 接続できる = can connect

This happens because 接続 is a verbal noun, and with many する verbs, the potential form is made with できる.

So:

• 利用する → 利用できる
• 予約する → 予約できる
• 接続する → 接続できる

This is a very common pattern.

Because 接続する / 接続できる usually marks the thing you connect to with に.

So:

• ワイファイに接続できる = can connect to Wi‑Fi

If you want to mention the device being connected, that device would often take を:

• スマホを無料のワイファイに接続できる
• You can connect your smartphone to the free Wi‑Fi

So in the original sentence, the device is simply omitted because it is understood from context.

There is no explicit subject, which is very normal in Japanese.

Depending on context, it could mean:

• you can connect
• we can connect
• people can connect
• your device can connect

Japanese often leaves out the subject when it is obvious or unimportant.

So the sentence is naturally understood as something like:

• At this café, you can connect to free Wi‑Fi

They are similar, but not the same.

• このカフェでは、無料のワイファイに接続できる。

  • plain statement about what is possible at this café
  • more neutral

• このカフェなら、無料のワイファイに接続できる。

  • adds contrast or selection
  • suggests this café, unlike some others
  • can sound like if you choose this café, then you can connect

So なら has more of a given that / if it’s this one feeling, while では is more straightforward.

Potential forms in Japanese can sometimes suggest:

• ability
• possibility
• circumstances allowing something

In this sentence, 接続できる most naturally means it is possible to connect because the café offers access.

It does not mainly sound like formal permission, such as someone personally allowing you to do it. It is more about availability:

• the Wi‑Fi is there
• connection is possible

So the nuance is closer to you can access it than you are allowed to access it.

Yes. ワイファイ is the standard katakana writing for Wi‑Fi in ordinary Japanese text.

You may also see:

• Wi‑Fi
• wifi in casual writing online

But ワイファイ is completely normal and easy to understand.

Yes, it is natural, but it sounds a little formal or technical because of 接続できる.

In everyday conversation, many people would more naturally say:

• このカフェなら、無料でワイファイが使える。
• このカフェなら、無料Wi‑Fiが使える。

These versions sound more like normal speech:

• ワイファイが使える = you can use the Wi‑Fi

The original sentence is still perfectly fine, especially in:

• written explanations
• tech-related contexts
• instructions
• customer information

The comma marks a pause after the topic/conditional phrase このカフェなら.

It helps separate:

• the setup: as for this café / if it’s this café
• the main statement: you can connect to free Wi‑Fi

Japanese commas are often used more flexibly than English commas, but here it makes the sentence easier to read and reflects a natural pause.

In normal Japanese writing, you would usually write this sentence without spaces:

このカフェなら、無料のワイファイに接続できる。

The spaces in your example are almost certainly there for learners, to make the parts easier to see.

So:

• with spaces = learner-friendly formatting
• without spaces = normal Japanese writing