Пусть кофе и крепкий, мне всё равно хочется ещё одну чашку.

In many sentences, пусть does mean let or may:

• Пусть он войдёт. = Let him come in.

But here it has a different use. In the pattern пусть ... , ... it can introduce a concession, meaning something like:

• granted that
• even if
• although

So Пусть кофе и крепкий, мне всё равно хочется ещё одну чашку means roughly:

• Granted, the coffee is strong, but I still want another cup.

This is a very natural Russian way to say yes, that may be true, but...

The и is part of a common concessive pattern:

• пусть X и Y, ...
• хотя X и Y, ...

It adds the sense of even though / although indeed.

So:

• Пусть кофе крепкий would already be understandable.
• Пусть кофе и крепкий sounds more idiomatic and complete in this concessive structure.

You can think of it as:

• Even if the coffee is strong...
• Although the coffee is strong...

A close synonym would be:

• Хотя кофе и крепкий, мне всё равно хочется ещё одну чашку.

This is a very common learner question.

In standard Russian, кофе is traditionally treated as a masculine noun, even though it ends in -е and looks like a neuter noun. So standard agreement is:

• крепкий кофе
• горячий кофе
• вкусный кофе

That is why the sentence has крепкий, not крепкое.

A few notes:

• кофе is indeclinable, so its form does not change by case.
• In colloquial modern Russian, some speakers do use neuter agreement, but masculine is the standard form learners are usually taught first.

In Russian, the verb to be is normally omitted in the present tense.

So:

• Кофе крепкий literally looks like coffee strong
• but it means The coffee is strong

That is completely normal Russian grammar.

If you put it into the past or future, a form of быть appears:

• Кофе был крепкий. = The coffee was strong.
• Кофе будет крепкий. = The coffee will be strong.

Both are possible, but they are not exactly the same in tone.

Я хочу

This is direct and straightforward:

• Я хочу ещё одну чашку. = I want another cup.

Мне хочется

This is more impersonal and softer. It often means:

• I feel like having
• I want
• I’m in the mood for

So мне хочется ещё одну чашку sounds a bit less forceful and more like a spontaneous desire.

In this sentence, мне всё равно хочется ещё одну чашку means something like:

• I still feel like having another cup anyway.

Because хочется is used in an impersonal construction.

Russian often expresses feelings or states with the experiencer in the dative:

• мне холодно = I am cold
• мне скучно = I am bored
• мне хочется кофе = I want / feel like coffee

So мне literally means something like to me, but in natural English we translate it as I:

• мне хочется = I want / I feel like

Here всё равно means:

• all the same
• anyway
• still
• regardless

So the logic is:

• the coffee is strong,
• but despite that,
• I still want another cup.

Examples:

• Мне всё равно. = I don’t care / It makes no difference to me.
• Он устал, но всё равно работает. = He is tired, but he is still working anyway.

In your sentence, всё равно strengthens the contrast: despite the fact that the coffee is strong, the speaker still wants more.

It is accusative case, because it is the thing wanted.

The basic noun is:

• одна чашка = one cup

But after хочется in this meaning, the object is in the accusative:

• хочется ещё одну чашку

Since чашка is feminine, one changes like this:

• nominative: одна чашка
• accusative: одну чашку

So:

• ещё одну чашку = another cup / one more cup

It can mean both, depending on context.

• ещё = still / yet / more / another
• одну чашку = one cup

Together, ещё одну чашку is naturally understood as:

• one more cup
• another cup

In English, another cup is usually the best translation here.

Yes, absolutely.

That version is very natural:

• Пусть кофе и крепкий, я всё равно хочу ещё одну чашку.

Compared with the original:

• я хочу is more direct.
• мне хочется is a little softer, more like I still feel like having another cup.

So both are correct, but they give slightly different shades of meaning.

Yes, the meaning is very close.

Compare:

• Пусть кофе и крепкий, мне всё равно хочется ещё одну чашку.
• Хотя кофе и крепкий, мне всё равно хочется ещё одну чашку.

Both mean something like:

• Although the coffee is strong, I still want another cup.

The version with пусть can sound a bit more like:

• Granted, the coffee is strong...
• Even if the coffee is strong...

So пусть often carries a stronger feeling of conceding a point before continuing.

The comma separates the concessive part from the main part.

Structure:

• Пусть кофе и крепкий = concessive clause
• мне всё равно хочется ещё одну чашку = main clause

So the comma works much like it would in English in a sentence such as:

• Although the coffee is strong, I still want another cup.

Russian word order is flexible, but this version is very natural.

Current order:

• Пусть кофе и крепкий, мне всё равно хочется ещё одну чашку.

This puts the concession first, then the main point.

You could also say:

• Мне всё равно хочется ещё одну чашку, пусть кофе и крепкий.

But that sounds a bit more marked or stylistically different.

Within the second part, word order can also shift slightly for emphasis:

• Мне всё равно хочется ещё одну чашку.
• Мне хочется ещё одну чашку всё равно. — possible, but less neutral
• Ещё одну чашку мне всё равно хочется. — emphasizes ещё одну чашку

For learners, the original word order is a very good model to follow.