Le due case si assomigliano.

Because case is a feminine plural noun.

• Singular: la casa = the house
• Plural: le case = the houses

So:

• le = the for feminine plural nouns
• due = two
• case = houses

Italian numbers usually go article + number + noun here: le due case.

Casa is a very common noun that changes like this:

• casa → singular
• case → plural

This is a normal pattern for many feminine nouns ending in -a:

• porta → porte
• strada → strade
• casa → case

One thing to watch out for: Italian case does not sound like the English word case.

Here si means something like each other.

So Le due case si assomigliano means:

• The two houses resemble each other
• or The two houses are similar to each other

This si is not really translated as themselves here. With a plural subject, it often has a reciprocal meaning: the two things do the action to each other.

Not in the usual wash oneself / see oneself sense. Here it is better understood as reciprocal.

• reflexive: the subject does something to itself
• reciprocal: two or more subjects do something to each other

So in this sentence:

• si assomigliano = they resemble each other

That is why the sentence sounds natural with two houses, but a singular version with this same reciprocal idea would not make sense.

Because the subject is plural: le due case = the two houses.

The verb comes from assomigliare and here it is in the present tense, 3rd person plural:

• io assomiglio = I resemble / I am similar
• tu assomigli
• lui/lei assomiglia
• noi assomigliamo
• voi assomigliate
• loro assomigliano

Since the subject is they (the two houses), Italian uses assomigliano.

Good question. The verb assomigliare often works with a when you say what something resembles:

• Questa casa assomiglia a quella. = This house resembles that one.

But in Le due case si assomigliano, the idea is already reciprocal: the two houses resemble each other. Because of that, you do not need to add a separate a phrase.

A useful comparison:

• Una casa assomiglia all’altra. = One house resembles the other.
• Le due case si assomigliano. = The two houses resemble each other.

Yes, absolutely.

• Le due case si assomigliano = The two houses resemble each other
• Le due case sono simili = The two houses are similar

Both are natural. The difference is mostly one of wording:

• sono simili is very straightforward: are similar
• si assomigliano focuses more on the idea of resembling each other

In many everyday situations, either one would work.

Because Italian usually does not need subject pronouns when the verb ending already shows who the subject is.

Here assomigliano already tells you the subject is they. And the noun phrase le due case is explicitly there anyway, so adding loro would be unnecessary in normal speech.

Italian often sounds more natural without subject pronouns unless you want emphasis or contrast.

Roughly: ahs-soh-MEE-lyah-no

A few notes:

• ss is pronounced clearly, like a stronger s
• gli is a special Italian sound; for English speakers, lyah is a useful approximation
• the stress is on -mi-: asso-MI-glia-no

And the whole sentence is roughly:

Le due case si assomigliano
→ leh DOO-eh KAH-zeh see ahs-soh-MEE-lyah-no

Not perfect English-style phonetics, but close enough to help you say it.