Mi bismo pozvali komšiju i komšinicu, ali oni sada rade.

Bismo is the conditional auxiliary for we. In English, it usually corresponds to would.

So:

• Mi bismo pozvali = We would invite

Serbian forms the conditional with:

• bih = I would
• bi = you would / he would / she would / it would
• bismo = we would
• biste = you would
• bi = they would

Then you add the main verb in its -l participle form.

Pozvali is the -l participle of pozvati.

In the Serbian conditional, you do not use a simple present form like pozovemo. Instead, you use:

• bismo
  • pozvali

So:

• Mi bismo pozvali = We would invite

Compare:

• pozovemo = we invite / let us invite / we will invite in certain contexts, but not the normal way to say we would invite
• bismo pozvali = we would invite

This is one of the core patterns in Serbian grammar.

Yes. The -l participle agrees with the subject in number and, in the plural, often also in gender.

Here, pozvali is masculine plural, which is also the default form for a mixed group.

So:

• Mi bismo pozvali = used if the speakers are male or mixed
• Mi bismo pozvale = used if the speakers are all female

An English speaker often misses this because English past participles do not change for gender.

Because they are direct objects, so they appear in the accusative case.

Dictionary forms are usually the nominative:

• komšija = neighbor (male)
• komšinica = neighbor (female)

In this sentence, they are the people being invited, so Serbian uses the accusative:

• komšiju
• komšinicu

So:

• pozvati komšiju i komšinicu = to invite the male neighbor and the female neighbor

Because some Serbian masculine nouns end in -a, especially words for male people.

So even though komšija looks like many feminine nouns in form, it is grammatically masculine because it refers to a man.

That is why its forms behave like a masculine animate noun:

• nominative: komšija
• accusative: komšiju

This is very common with words such as:

• sudija = judge
• gazda = boss/owner
• vođa = leader

The sentence is being specific: it means one male neighbor and one female neighbor.

So Serbian uses:

• komšiju = the male neighbor
• komšinicu = the female neighbor

If you used a plural like komšije, that would mean neighbors in a more general way, without spelling out one man and one woman separately.

So this sentence is explicitly mentioning both individuals.

Yes. Serbian often drops subject pronouns when the verb already makes the person clear.

So both are possible:

• Mi bismo pozvali komšiju i komšinicu, ali oni sada rade.
• Bismo pozvali komšiju i komšinicu, ali oni sada rade.

However, in real Serbian, Mi is often kept for emphasis or contrast. Here it helps create a contrast with oni later:

• Mi bismo pozvali..., ali oni sada rade.

That sounds a bit like:

• We would invite them, but they are working now.

Because in Serbian, a mixed-gender group normally takes the masculine plural form.

So if they refers to:

• one man + one woman

the pronoun is:

• oni

This is the standard masculine/mixed plural pronoun.

Compare:

• oni = they (masculine or mixed)
• one = they (all feminine)
• ona = they (neuter things/abstracts, much less relevant here)

Since komšija + komšinica is a mixed pair, oni is exactly what you expect.

Because Serbian does not have a separate present continuous form like English are working.

It simply uses the present tense:

• rade

Depending on context, this can mean:

• they work
• they are working

Here, the word sada = now makes it clear that the action is happening at this moment:

• oni sada rade = they are working now

This is a very important difference between English and Serbian.

Both mean now.

• sada is a bit more full and neutral
• sad is a very common shorter form, especially in everyday speech

So these would both be natural:

• oni sada rade
• oni sad rade

There is no major meaning difference here. It is mostly a matter of style and rhythm.

Yes, Pozvali bismo... is also correct.

The key point is that bismo is a clitic, and Serbian clitics usually go in the second position of the clause.

So you can have:

• Mi bismo pozvali...
• Pozvali bismo...

In the first version, mi comes first, so bismo comes right after it.

In the second version, pozvali comes first, so bismo follows that.

Both are grammatical, but the choice affects emphasis:

• Mi bismo pozvali... emphasizes we
• Pozvali bismo... sounds a bit more neutral in many contexts

Because pozvati is the perfective verb, and it fits the idea of one complete act of inviting.

Serbian often distinguishes between:

• zvati = imperfective
• pozvati = perfective

Here, the sentence means something like we would invite them as a single complete action, so pozvati is the natural choice.

Very roughly:

• pozvati = to invite/call once, as a completed act
• zvati = to call/invite in a more ongoing, repeated, or general sense

So:

• Mi bismo pozvali... = We would invite...
  sounds like one complete invitation

That is why the perfective verb is preferred here.