На этом стуле неудобно сидеть.

Because Russian uses на with things you sit on, such as chairs, benches, sofas, and stools.

• на стуле = on a chair
• на диване = on a sofa
• на скамейке = on a bench

Using в would mean in, which does not fit a normal chair.

Because на here requires the prepositional case when it means location.

• dictionary form: стул = chair
• prepositional singular: на стуле = on the chair

So:

• стул → nominative
• на стуле → prepositional after на

Этом is the prepositional singular masculine/neuter form of этот (this).

It has to agree with стуле, which is:

• masculine
• singular
• in the prepositional case

So:

• этот стул = this chair
• на этом стуле = on this chair

Here неудобно means uncomfortably / it is uncomfortable in an impersonal construction.

It is not describing the chair with an adjective like неудобный стул (an uncomfortable chair). Instead, it describes the situation or activity:

• На этом стуле неудобно сидеть.
• Literally: On this chair, it is uncomfortable to sit.

This use is very common in Russian:

• трудно понять = it is hard to understand
• интересно читать = it is interesting to read
• удобно работать = it is convenient to work

Because неудобный is an adjective, and adjectives describe nouns.

For example:

• неудобный стул = an uncomfortable chair

But in your sentence, Russian is not directly saying this is an uncomfortable chair. It is saying:

• it is uncomfortable to sit on this chair

That is why Russian uses неудобно instead of неудобный.

Compare:

• Это неудобный стул. = This is an uncomfortable chair.
• На этом стуле неудобно сидеть. = It is uncomfortable to sit on this chair.

Russian often uses impersonal sentences where English needs a dummy subject like it.

English says:

• It is uncomfortable to sit on this chair.

Russian simply says:

• На этом стуле неудобно сидеть.

There is no need for a word meaning it here. The sentence is grammatically complete without one.

Because the sentence expresses a general idea: to sit on this chair is uncomfortable.

The structure is:

• [place / context] + неудобно + infinitive

So:

• неудобно сидеть = it is uncomfortable to sit
• трудно работать = it is hard to work
• приятно отдыхать = it is pleasant to relax

The infinitive names the activity itself.

Сидеть is the imperfective verb, and it refers to the ongoing state or activity of sitting.

That fits the meaning here: the sentence is about being seated on the chair, not about the one-time action of sitting down.

• сидеть = to sit, to be sitting
• сесть = to sit down

So:

• На этом стуле неудобно сидеть. = It is uncomfortable to sit on this chair.
• На этот стул неудобно сесть. = It is uncomfortable / awkward to sit down on this chair.

That second sentence has a different meaning and would usually imply the action of getting seated, not the experience of remaining seated.

Yes. Russian word order is flexible.

These are all natural, though the emphasis changes slightly:

• На этом стуле неудобно сидеть.
• На этом стуле сидеть неудобно.
• Сидеть на этом стуле неудобно.

The version you gave is very natural and neutral.

A rough idea of the emphasis:

• На этом стуле неудобно сидеть. → starts with the place: on this chair
• Сидеть на этом стуле неудобно. → starts with the activity: sitting on this chair

Strictly speaking, it describes the experience of sitting on it.

That often implies that the chair itself is uncomfortable, but grammatically the sentence is about the action/situation:

• неудобно сидеть = sitting is uncomfortable

So the focus is not exactly the noun chair, but the whole situation of using it in that way.

Yes, absolutely.

• Мне неудобно сидеть на этом стуле. = It is uncomfortable for me to sit on this chair.

Adding мне makes the experiencer explicit: for me.

Without мне, the statement is more general:

• На этом стуле неудобно сидеть. = It is uncomfortable to sit on this chair. / This chair is uncomfortable to sit on.

With мне, it becomes more personal:

• Мне неудобно сидеть на этом стуле. = I find it uncomfortable to sit on this chair.

Неудобно is normally written as one word because it functions as a single lexical item meaning uncomfortably / inconveniently / not comfortably.

In most ordinary cases, you write:

• удобно = comfortable, convenient
• неудобно = uncomfortable, inconvenient

Writing не удобно separately is much less common and usually only happens in special contrastive contexts.

For a learner, the safe default here is:

• неудобно — one word

In this sentence, yes, it most naturally means physically uncomfortable.

But in other contexts, неудобно can also mean:

• inconvenient
• awkward
• embarrassing in some situations

Examples:

• Мне неудобно ехать завтра. = It is inconvenient for me to go tomorrow.
• Мне неудобно спрашивать. = I feel awkward asking.

In На этом стуле неудобно сидеть, the meaning is clearly physical comfort.