Learn Hardcore German: Manchmal fühlt sich das Alte sehr gemütlich an.

fühlen = to feel (actively, with your senses or emotions)
- Ich fühle Kälte. – I feel cold (I perceive cold).
sich anfühlen = to feel (like), describing how something feels to the touch or in experience
- Das Alte fühlt sich gemütlich an. – The old stuff feels cozy.

In your sentence, we are not talking about someone feeling something, but about how something feels. For that, German normally uses sich anfühlen, not plain fühlen.

So fühlt sich … an is the normal pattern for:
[subject] + feels [adjective] → [Subjekt] + fühlt sich [Adjektiv] an.

What does the sich in fühlt sich an do? Why is it there?

sich is the reflexive pronoun that belongs to the verb sich anfühlen.

Think of sich anfühlen as one unit, similar to English to feel in “It feels nice.”
In German we literally say “It feels itself nice”, with sich marking that reflexive structure:

Es fühlt sich weich an. – It feels soft.
Das Alte fühlt sich gemütlich an. – The old (stuff) feels cozy.

You normally cannot omit sich here; ✗ Es fühlt gemütlich an is wrong.

Why is an at the very end of the sentence?

anfühlen is a separable verb (trennbares Verb). In the present tense main clause, the prefix an goes to the end:

Infinitive: sich anfühlen
Main clause:
- Es fühlt sich gemütlich an.
- Manchmal fühlt sich das Alte sehr gemütlich an.

Pattern:
[other elements] + finite verb + (reflexive pronoun, objects, adverbs…) + separable prefix

So fühlt (the conjugated part) comes in the second position, and an (the prefix) goes to the end.

What exactly is das Alte? Why is Alte capitalized and why is it neuter (das)?

das Alte is a nominalized adjective: an adjective used as a noun.

alt = old (adjective)
das Alte = the old (thing / things / stuff / what is old)

When German turns an adjective into a noun like this, the adjective is capitalized: Alte.

The neuter article das here gives a general, abstract meaning:
das Alte ≈ the old things / the old stuff / what is old in a broad, non‑specific sense.

So the sentence means roughly:
Sometimes the old (things/ways/stuff) feel very cozy.

Could I also say die Alte or der Alte instead of das Alte?

Grammatically yes, but the meaning changes a lot:

die Alte (feminine, singular) in everyday speech usually means the old woman (often rude or very colloquial).
der Alte (masculine, singular) can mean the old man, sometimes also the old boss / the old guy (also informal/colloquial).

das Alte is neutral and abstract: the old (things).
Using der Alte or die Alte here would sound like you are talking about a specific old man or woman, not about “old things” in general. That would not fit your sentence’s meaning.

What case is das Alte in here, and how can I tell?

das Alte is in the nominative case, because it is the subject of the sentence.

Structure:

Manchmal – adverb (Sometimes)
fühlt – verb (3rd person singular)
sich – reflexive pronoun
das Alte – subject: what feels cozy? → das Alte
sehr gemütlich – predicate adjective phrase
an – separable prefix of the verb

The thing that “does” the feeling (or is described as feeling some way) is das Alte, so it must be nominative.

Why is fühlt in the 3rd person singular form?

The verb fühlt is the 3rd person singular form of fühlen (here as part of sich anfühlen).

Conjugation (present tense):

ich fühle
du fühlst
er / sie / es fühlt
wir fühlen
ihr fühlt
sie fühlen

The subject is das Alte, which is third person singular neuter (es).
So we need es fühlt → das Alte fühlt.

Can I move manchmal to a different place, like Das Alte fühlt sich manchmal sehr gemütlich an?

Yes, that is possible and correct:

Manchmal fühlt sich das Alte sehr gemütlich an.
- Emphasis on “Sometimes…” (time first).
Das Alte fühlt sich manchmal sehr gemütlich an.
- Starts with “The old (stuff)…”, the time information is more in the middle.

German main clauses are verb‑second. Both sentences respect this:

Manchmal (1st element) – fühlt (2nd element, the finite verb) – …
Das Alte (1st element) – fühlt (2nd element) – …

So you can move manchmal as long as you keep the verb in the second position (and the rest of the word order intact).

Why is it sehr gemütlich and not something like viel gemütlich?

In German:

sehr is used to intensify adjectives and adverbs:
- sehr gemütlich – very cozy
- sehr schön, sehr schnell, sehr teuer
viel is mainly used with verbs or uncountable nouns to mean a lot / much:
- viel essen, viel arbeiten, viel Zeit, viel Geld

So with an adjective like gemütlich, the standard intensifier is sehr, not viel.
✗ viel gemütlich is wrong in standard German.

Could I say Manchmal ist das Alte sehr gemütlich instead of fühlt sich … an? What is the difference?

You can say:

Manchmal ist das Alte sehr gemütlich.

This is grammatically correct and means:

Sometimes the old (things) are very cozy.

However, there is a nuance difference:

ist gemütlich – describes a quality/state: the old things are cozy (in general).
fühlt sich gemütlich an – focuses more on how they feel to you in experience or to the senses.

In many contexts they can overlap, but fühlt sich gemütlich an slightly emphasizes your perception of the coziness.

What does gemütlich really mean? Is it just “comfortable”?

gemütlich is often translated as cozy, homely, or comfortable, but it carries a bit more of a cultural flavor:

physically comfortable (soft chair, warm room)
emotionally pleasant, relaxed atmosphere
inviting, warm, not stressful

Examples:

ein gemütliches Zimmer – a cozy, homely room
ein gemütlicher Abend – a relaxed, pleasant evening
eine gemütliche Kneipe – a cozy pub with a friendly atmosphere

gemütlich is more about cozy, relaxed atmosphere and comfort together, not just the physical comfort alone.