Иногда бывают чудеса.

Бывают is the 3rd person plural present form of бывать.

In this sentence, it means something like:

• do happen
• do occur
• there are sometimes

So Иногда бывают чудеса is very naturally understood as Sometimes miracles happen.

A useful nuance:

• быть = to be
• бывать = to be / occur from time to time, often with a sense of repeated or occasional occurrence

That is why бывают works especially well with иногда (sometimes).

Because есть is usually not the best choice for this kind of idea.

Compare:

• Иногда бывают чудеса. = Sometimes miracles happen / occur.
• Иногда есть чудеса. = grammatically odd in most contexts

Russian often uses бывать for things that occur occasionally, especially in general statements. With events, phenomena, strange situations, exceptions, and so on, бывают sounds much more natural than есть.

So this sentence is not just saying that miracles exist; it is saying that they do occur sometimes.

Чудеса is the plural of чудо.

So:

• чудо = miracle
• чудеса = miracles

Using the plural here gives a general statement: miracles are something that sometimes happen.

Compare:

• Иногда бывает чудо. = Sometimes a miracle happens.
• Иногда бывают чудеса. = Sometimes miracles happen.

The plural sounds a bit more like a broad truth or observation, while the singular can sound more like one miracle at a time.

Because the verb agrees with чудеса, which is plural.

• чудо → singular → бывает
• чудеса → plural → бывают

So:

• Иногда бывает чудо.
• Иногда бывают чудеса.

Even though чудеса comes after the verb, it is still the noun that the verb agrees with.

Yes.

In English, we usually expect the subject before the verb, but Russian word order is much freer. In sentences that introduce the existence or occurrence of something, Russian often puts the verb first and the noun after it.

So in:

• Иногда бывают чудеса

the noun чудеса is still the thing being talked about, even though it comes after бывают.

This verb-first order feels natural for a meaning like:

• there are sometimes miracles
• sometimes miracles happen

Yes. Russian allows several word orders, but they do not all sound equally neutral.

These are all possible:

• Иногда бывают чудеса.
• Чудеса иногда бывают.
• Иногда чудеса бывают.

The version you were given is very natural and neutral.

A rough guide:

• Иногда бывают чудеса. → neutral, presentational: Sometimes miracles happen.
• Чудеса иногда бывают. → stronger focus on miracles
• Иногда чудеса бывают. → possible, but can sound more contrastive or stylistically marked depending on context

So the original order is a very good default.

It is nominative plural.

Dictionary form:

• чудо = nominative singular

Here:

• чудеса = nominative plural

It is not an object here. The sentence is not saying that someone does something to miracles. It is saying that miracles occur.

Also, чудеса is a somewhat irregular-looking plural form, which learners often notice:

• чудо → чудеса

This pattern also appears in some other neuter nouns, for example:

• слово → слова
• дело → дела

The stress is:

• иногда́
• быва́ют
• чудеса́

So the full sentence is:

Иногда́ быва́ют чудеса́.

A couple of pronunciation notes:

• Unstressed о is usually pronounced more like a in Russian.
• In бывают, the ю is not present; it is -ают, pronounced roughly -ayut.
• Final stressed -са́ in чудеса́ is important; do not stress the first syllable there.

Yes, absolutely.

• Иногда бывают чудеса.
• Иногда случаются чудеса.

Both can mean Sometimes miracles happen.

The difference is mostly one of nuance:

• случаться = to happen
• бывать = to occur / to exist from time to time

So случаются чудеса is more directly miracles happen, while бывают чудеса can feel a little broader or more idiomatic, almost like such things do occur sometimes.

Both are good Russian.

Because Russian does not have articles like English a/an and the.

So чудеса by itself can mean simply miracles, and the exact shade of definiteness comes from context.

In this sentence, the meaning is generic:

• miracles in general
• not specific miracles already mentioned

That is why the Russian sentence works perfectly without any article-like word.