У сусідів є немовля, а в моєї подруги — близнюки.

This sentence uses the common Ukrainian possession pattern:

у / в + possessor in the genitive + є + thing possessed in the nominative

So:

• У сусідів є немовля = literally At the neighbors there is a baby
• в моєї подруги — близнюки = literally at my friend’s — twins

This is how Ukrainian very often expresses have/has.

Ukrainian can use мати for to have, but in everyday speech possession is very often expressed with the у/в ... є ... structure instead.

So English They have a baby is very naturally: У них є немовля

and not necessarily: Вони мають немовля

Using у/в ... є ... sounds very normal and idiomatic here.

У and в are just two euphonic variants of the same preposition here. Ukrainian often switches between them to make pronunciation smoother.

In this sentence:

• У сусідів sounds natural at the start of the sentence
• after а, using в моєї подруги flows better than у моєї подруги

So the choice is mainly about sound, not meaning.

Because after у/в in this possession pattern, the possessor goes in the genitive case.

The dictionary form is сусіди = neighbors.
Here it becomes сусідів = of the neighbors / at the neighbors’ place.

So:

• nominative: сусіди
• genitive plural: сусідів

For the same reason: the possessor must be in the genitive after у/в.

The base form is:

• моя подруга = my female friend

In the genitive singular it becomes:

• моєї подруги

Both words change because моєї must agree with подруги in case, number, and gender.

They are in the nominative case.

In this structure, the thing that exists or is possessed is normally in the nominative:

• є немовля
• є близнюки

So even though English might make you think of a direct object after have, Ukrainian is not building the sentence that way. It is more like there is/there are.

In the second clause, є is simply omitted because it is understood from the first clause.

The full version would be:

У сусідів є немовля, а в моєї подруги є близнюки.

But Ukrainian often leaves out repeated words when they are obvious. That makes the sentence more natural and less repetitive.

The dash marks the place where something has been omitted, here basically є.

So:

а в моєї подруги — близнюки

means roughly:

and my friend has twins
or more literally
and at my friend’s — twins

The dash is very common in Ukrainian when the second part of a sentence leaves out a repeated verb or predicate.

Yes. You can say the full version:

а в моєї подруги є близнюки

That is completely correct.

The version with the dash is shorter and stylistically neat because it avoids repeating є. Both are grammatical; the dashed version is just more compact.

Близнюки means twins, so it is naturally plural.

The singular form is близнюк = a twin.
But when talking about the pair, Ukrainian normally uses the plural:

• У них є близнюки = They have twins

So in this sentence, близнюки is nominative plural.

Yes: немовля is a neuter noun meaning baby / infant.

In the nominative singular it is:

• немовля

That is why the sentence says:

• є немовля

Its form may look unusual if you are expecting a more typical noun ending, but it is a normal Ukrainian noun. Here it is simply the nominative singular form.