Learn Hardcore Russian: Мне не хватает тишины в этом кафе.

With (не) хватать Russian usually uses an impersonal structure: [to someone — dative] + (не) хватает + [of something — genitive].
So мне не хватает... literally means to me there isn’t enough... / I’m lacking..., not I (subject) don’t have....

Why do we say не хватает (3rd person singular) and not не хватаю?

Because хватает here is impersonal: there is no grammatical subject like я. It behaves like нужно / можно / нельзя in that sense. The “thing that’s missing” is not the subject either; it’s expressed in the genitive.

Why is тишины in the genitive case?

After (не) хватать, the thing that is lacking is typically in the genitive:

мне хватает времени = I have enough time
мне не хватает времени = I don’t have enough time
So тишины is genitive singular of тишина.

What’s the difference between мне не хватает тишины and мне нужна тишина?

Both can be translated as I need quiet, but the nuance differs:

мне нужна тишина = I need quiet (a direct need/request; more “I want it to be quiet”)
мне не хватает тишины = I’m lacking quiet / there isn’t enough quiet (emphasizes a shortage compared to what you expect)

Can I use nominative and say мне не хватает тишина?

No. With (не) хватает, nominative doesn’t work in standard Russian. It should be тишины (genitive).

Why is it в этом кафе and not в этот кафе?

After в meaning in (a place), Russian uses the prepositional case: в кафе, в этом кафе.
этот changes to этом to match prepositional masculine/neuter.

Does кафе decline? Why does it look the same?

кафе is an indeclinable noun (a loanword). Its form stays the same in all cases: в кафе, из кафе, к кафе, etc. The adjective still declines: в этом кафе, в хорошем кафе.

Is the word order fixed? Can I move в этом кафе?

It’s flexible. These are all natural, with slight emphasis changes:

Мне не хватает тишины в этом кафе. (neutral; the café is where you miss quiet)
В этом кафе мне не хватает тишины. (sets the scene first; contrast with other places)
Мне в этом кафе не хватает тишины. (slightly tighter link between me + this café)

Is не always used with хватает like this? How does the positive version look?

The positive is the same structure without не:

Мне хватает тишины в этом кафе. = There’s enough quiet for me in this café / I find it quiet enough here.
With не, it becomes a shortage.

Could I replace не хватает with another verb like недостаёт?

Yes. мне не хватает тишины and мне недостаёт тишины are close in meaning. не хватает is more common in everyday speech; недостаёт can sound a bit more formal or stylistic depending on context.

Does тишины mean “silence” or “quiet”?

тишина covers both silence and quietness, depending on context. In a café, it usually means quiet / a quieter atmosphere, not absolute silence.

Can this sentence imply “I miss silence” emotionally, like nostalgia?

It can, but by default it’s practical: it’s too noisy here.
If you want a stronger “I miss it (in general)” feel, you might add context, e.g. Мне в последнее время не хватает тишины (Lately I’ve been missing quiet).