kono su de saezutte iru tori ha suzume ni tigai nai.

It breaks down like this:

この巣で = at/in this nest
さえずっている = is chirping
鳥 = bird
は = topic marker
雀に違いない = must be a sparrow

So the overall structure is:

[この巣でさえずっている鳥] は [雀に違いない]

In other words, the bird that is chirping at this nest must be a sparrow.

This is a Japanese relative clause.

In English, you say:

the bird that is chirping

In Japanese, the clause simply comes before the noun:

さえずっている鳥

Literally, this is something like:

chirping bird

or more naturally:

the bird that is chirping

Japanese does not need a relative pronoun like that, which, or who here.

Because で marks the place where an action happens.

Here, the action is さえずる = to chirp. So:

この巣でさえずっている = chirping at/in this nest

By contrast, に often marks the place where something exists or ends up.

Compare:

この巣でさえずっている鳥
= the bird chirping at this nest

この巣にいる鳥
= the bird that is in this nest

So で focuses on the location of the chirping, while に would focus on the bird’s location or existence.

It comes from the dictionary form さえずる, which means to chirp or to twitter.

Its て-form is さえずって, and adding いる gives:

さえずっている

This is the -ている form, which often shows an ongoing action.

So:

さえずる = to chirp
さえずっている = is chirping

In casual speech, you may also hear さえずってる.

Here, -ている shows an ongoing action or a current state.

So さえずっている means:

is chirping
chirping

When this form modifies a noun, it often sounds like English -ing or that is ...ing:

さえずっている鳥
= the bird that is chirping
= the chirping bird

In this sentence, it most naturally suggests that the bird is currently chirping.

は marks 鳥 as the topic of the main sentence.

So the sentence is saying:

As for the bird chirping at this nest, it must be a sparrow.

This is a very normal way to present information in Japanese.

If you used が instead, the nuance would shift more toward identifying or emphasizing the subject itself. With は, the sentence sounds more like a general statement about that bird.

に違いない is a grammar pattern meaning:

must be
there is no doubt that it is
cannot be anything but

So:

雀に違いない = must be a sparrow

With a noun, the pattern is:

noun + に違いない

Examples:

彼は先生に違いない。
= He must be a teacher.

あれは夢に違いない。
= That must be a dream.

The idea is strong certainty based on evidence or inference.

It is quite strong. It expresses the speaker’s confidence that something is true.

So 雀に違いない is stronger than a simple guess like:

雀だろう = it is probably a sparrow

It is often closer to:

It must be a sparrow
It has to be a sparrow
It is almost certainly a sparrow

This is not the must of obligation, like You must go. It is the must of logical conclusion.

Not necessarily.

Because で marks the place where the action happens, この巣でさえずっている means the chirping is happening at, in, or around this nest, depending on context.

So in English, translations like these could all work depending on the situation:

the bird chirping in this nest
the bird chirping at this nest
the bird chirping from this nest

If you specifically want to say the bird is located in the nest, この巣にいる鳥 would make that clearer.

鳴く is a general verb for animals making sounds.

さえずる is more specific and is used for the chirping, twittering, or warbling of small birds.

So:

鳥が鳴く = a bird makes a sound / sings / chirps
鳥がさえずる = a bird chirps or twitters

Using さえずる gives a more specific and vivid image than 鳴く.

Yes, but the meaning would change slightly.

この巣にいる鳥は雀に違いない
= The bird that is in this nest must be a sparrow.

That version focuses on where the bird is.

The original:

この巣でさえずっている鳥は雀に違いない
focuses on what the bird is doing at this nest.

So the original gives more descriptive information.

It is read:

この す で さえずって いる とり は すずめ に ちがい ない。

Without learner spacing, it would normally be written as:

この巣でさえずっている鳥は雀に違いない。

Useful readings:

巣 = す
鳥 = とり
雀 = すずめ
違いない = ちがいない