Пусть мандарин и маленький, после ужина мне хочется именно его, а не большой десерт.

That is one of its meanings, but not in this sentence.

Here пусть introduces a concessive idea: even if, granted that, or let it be so. So:

• Пусть мандарин и маленький, ...
  = Even if the mandarin is small, ... = Granted, the mandarin is small, but ...

So it is not giving an order. It is acknowledging a fact and then contrasting it with the speaker’s real point.

Right — here и is not a simple and.

In the pattern пусть ... и ..., the и helps create a concessive meaning:

• Пусть мандарин и маленький
  = The mandarin may be small, but... = Even though the mandarin is small...

You will see the same thing with хотя too:

• Хотя он и устал, он работает.
  = Although he is tired, he is working.

So in this sentence, и is part of the yes, that may be true, but... structure.

Маленький is a predicate adjective describing мандарин:

• мандарин маленький = the mandarin is small

Russian usually does not use a present-tense verb to be in sentences like this. So English is is simply omitted:

• Он высокий. = He is tall.
• Мандарин маленький. = The mandarin is small.

As for the form, маленький agrees with мандарин, which is masculine singular, so the adjective is also masculine singular.

Because после requires the genitive case.

The noun is ужин (dinner), and its genitive singular form is ужина:

• после ужина = after dinner

This is just a standard preposition + case pattern you need to learn:

• после работы = after work
• после фильма = after the film
• после ужина = after dinner

Because мне хочется is softer and more about a feeling or craving.

• я хочу = I want
• мне хочется = I feel like, I’m in the mood for, I have a desire for

Literally, мне хочется is an impersonal construction: to me, it is wanted / to me, it feels desirable.

That is why мне is in the dative case:

• мне хочется чаю = I feel like some tea
• мне хочется спать = I feel like sleeping / I’m sleepy
• мне хочется именно его = I specifically feel like that one

So this sentence sounds more natural for a post-dinner preference or craving than a plain я хочу.

Именно adds focus: exactly, precisely, specifically.

So:

• мне хочется именно его
  = I want specifically that one = That is exactly what I feel like

It strengthens the contrast with the next part:

• именно его, а не большой десерт
  = that specifically, not a big dessert

Without именно, the sentence would still work, but the contrast would be less pointed.

Here его means it (referring back to мандарин), not his.

So this is an object pronoun, not a possessive adjective.

A tricky point is that его has the same form in more than one role:

• possessive: его книга = his book
• object pronoun: я вижу его = I see him/it

In this sentence, it is clearly the object pronoun because it means the mandarin as the thing desired.

As for case: with хочется, Russian can use different patterns, and его happens to look the same in both accusative and genitive. So the form itself does not tell you much. What matters most for a learner here is:

• его refers to мандарин
• it means it / that one
• it is the object of хочется

Because а is very common when contrasting two alternatives:

• this, not that
• one thing, rather than another

So:

• именно его, а не большой десерт
  = that specifically, not a big dessert

Но is more like but in the sense of contradiction or unexpected opposition.
А is often better for side-by-side contrast.

Compare:

• Он устал, но работает.
  = He is tired, but he is working.
• Я хочу чай, а не кофе.
  = I want tea, not coffee.

This sentence is clearly the second type.

Because here the sentence is presenting большой десерт as the contrasting object: not a big dessert.

For a masculine inanimate noun like десерт, the accusative singular looks exactly like the nominative:

• nominative: большой десерт
• accusative: большой десерт

So even though it is functioning as the object, the form does not change.

If you saw большого десерта, that would be genitive. Russian can sometimes use genitive with verbs of wanting, but this sentence is using the more concrete, specific-object wording.

There are two commas for two different reasons.

1. After маленький
   The first part is a concessive clause:

• Пусть мандарин и маленький, ...

This is like Even if the mandarin is small, ..., so it is separated from the main clause with a comma.

2. Before а не большой десерт
   А is a coordinating conjunction, and in Russian it is normally preceded by a comma:

• ..., именно его, а не большой десерт.

So the punctuation reflects the structure:

• concessive opening
• main statement
• contrastive alternative