Non oltrepassare il cancello: il cane abbaia forte.

Because this is a negative command. In Italian, the negative imperative for tu is usually non + infinitive:

• Non parlare = Don’t speak
• Non andare = Don’t go
• Non oltrepassare = Don’t go past / Don’t cross

Also, on signs and warnings, Italian often uses the infinitive because it sounds neutral and impersonal, so non oltrepassare is very natural in that context.

Oltrepassare means to go beyond, to pass beyond, or to cross past a limit.

In this sentence, it means not to go past the gate. It is a bit stronger and more specific than just passare, because it suggests crossing a boundary.

Related verbs:

• passare = to pass
• superare = to surpass / get past / exceed
• varcare = to cross a threshold, gate, doorway

So non oltrepassare il cancello is basically warning you not to go beyond that point.

Because cancello means gate, while porta means door.

Use cancello for something like:

• a gate to a garden
• a gate at the entrance to a property
• a metal gate in a fence

Use porta for a door in a building or room.

So if the sentence is about entering a property or enclosed area, cancello is the right word.

The colon introduces the reason for the warning.

So the structure is:

• Non oltrepassare il cancello = warning / command
• il cane abbaia forte = explanation

It works like:

• Do not go past the gate: the dog barks loudly

In English, you could also use a dash or a full stop, but the colon neatly shows that the second part explains the first.

Italian usually uses an article with common nouns much more often than English does.

Here il cane means the dog, referring to a specific dog, probably the one behind the gate.

Compare:

• il cane abbaia = the dog barks
• un cane abbaia = a dog is barking / a dog barks

Using il makes it sound like a known, identifiable dog.

Because Italian often drops subject pronouns when they are not needed.

The verb form abbaia already tells you it is he/she/it barks, and the subject is explicitly given as il cane, so adding lui would be unnecessary.

That is very normal in Italian:

• Il cane abbaia = The dog barks
  not usually
• Il cane lui abbaia

Italian prefers the shorter version unless there is special emphasis.

Abbaia is the third person singular present tense of abbaiare, meaning to bark.

So:

• io abbaio = I bark
• tu abbai
• lui/lei abbaia = he/she barks

With il cane, the correct form is abbaia.

It can mean either, depending on context.

Italian often uses the simple present for both:

• a habitual action: the dog barks
• something happening now: the dog is barking

In this warning sentence, it most likely means something like:

• the dog barks loudly
• or the dog is barking loudly

If you wanted to be very explicit about the action happening right now, you could say il cane sta abbaiando.

Because in Italian, forte is very commonly used adverbially with verbs of sound, and it means loudly.

So these are natural:

• parlare forte = to speak loudly
• gridare forte = to shout loudly
• abbaiare forte = to bark loudly

Fortemente usually means strongly or intensely, and it would sound less natural here.

So il cane abbaia forte is the normal way to say that the dog barks loudly.

No, not in this sentence.

Although forte can mean strong, here it describes how the dog barks, so it means loudly.

So:

• un cane forte = a strong dog
• il cane abbaia forte = the dog barks loudly

Same word, different function.

It is understandable and correct, but there are other very natural ways to express the same warning.

For example:

• Non varcare il cancello = Do not cross the gate
• Non entrare = Do not enter
• Attenti al cane = Beware of the dog
• Non oltrepassare il cancello: il cane abbaia forte = Do not go past the gate: the dog barks loudly

Your sentence is fine, and oltrepassare gives a clear idea of not going beyond that boundary. On an actual sign, though, Italians might often choose a shorter warning such as Attenti al cane.