В этом кресле мне удобнее читать, чем на диване.

This is mostly a matter of normal Russian usage with these nouns:

• в кресле = in an armchair
• на диване = on a sofa / couch

Russian often treats an armchair as something you sit in, but a sofa as something you sit on. English does something similar: we say in a chair / armchair but on a sofa / couch.

Both phrases are about location here, just with different prepositions.

Because after в when it means in / at a location, Russian usually uses the prepositional case.

So:

• это кресло = this armchair (dictionary/basic form)
• в этом кресле = in this armchair

Here:

• кресло is neuter
• the prepositional singular form of этот for neuter is этом
• the prepositional singular of кресло is кресле

So в этом кресле literally means in this armchair.

Because the sentence describes a place where something happens, not motion toward it.

Compare:

• на диване = on the sofa / while on the sofa → location
• на диван = onto the sofa → motion/direction

In this sentence, the speaker is comparing two places for reading, so Russian uses the prepositional case:

• диван → на диване

Because Russian often uses the dative to show the person who experiences a feeling or situation.

So:

• мне удобно = it is comfortable for me
• мне удобнее = it is more comfortable for me

This is a very common Russian pattern. Instead of saying something like I am more comfortable reading..., Russian often says something closer to:

• To me, it is more comfortable to read...

That is why you get мне, not я.

Удобнее is the comparative form of удобный / удобно and means:

• more comfortable
• more convenient
• sometimes easier, depending on context

In this sentence, it means something like:

• It’s more comfortable for me to read...
• It’s more convenient for me to read...

Russian often uses this comparative in an impersonal way, without a subject like it.

Because Russian commonly uses an infinitive after words like удобно, трудно, легко, приятно, интересно, and their comparatives.

So:

• мне удобно читать = it is comfortable/convenient for me to read
• мне удобнее читать = it is more comfortable/convenient for me to read

The infinitive names the action in a general way. Russian is not saying I read here; it is saying to read.

Because in the present tense, Russian normally leaves out to be.

So where English says:

• It is more comfortable for me to read...

Russian simply says:

• мне удобнее читать...

There is no present-tense есть here. That is normal.

Чем means than in comparisons.

So:

• удобнее ..., чем ... = more comfortable ..., than ...

In this sentence:

• В этом кресле мне удобнее читать, чем на диване.
• It’s more comfortable for me to read in this armchair than on the sofa.

This is the standard way to make comparisons after a comparative form like удобнее, лучше, хуже, быстрее, etc.

Because Russian often leaves out words that are already understood from the first part.

The full idea is something like:

• В этом кресле мне удобнее читать, чем (мне удобнее читать) на диване.

But that would sound repetitive. So Russian keeps only what is necessary:

• ..., чем на диване

English does the same:

• It’s more comfortable for me to read in this armchair than on the sofa.

We do not need to repeat for me to read after than.

No, Russian word order is fairly flexible. This version puts emphasis first on the place:

• В этом кресле мне удобнее читать, чем на диване.

A different but still natural order would be:

• Мне удобнее читать в этом кресле, чем на диване.

The meaning stays basically the same, but the focus shifts a little:

• starting with В этом кресле highlights the armchair first
• starting with Мне удобнее highlights the speaker’s experience first

Yes, более удобно is possible in principle, but удобнее is much more natural here.

Russian often prefers the simple comparative form when it exists:

• удобно → удобнее
• быстро → быстрее
• легко → легче

So in this sentence, удобнее is the normal choice.