Learn Hardcore Icelandic: Eftir klukkutíma líður honum næstum eins og áður.

Eftir = after/in (a certain time from now)
klukkutíma = an hour (accusative singular of the compound klukkutími, clock+time)
líður = feels/goes (3rd person singular present of að líða)
honum = to him (dative of hann)
næstum = almost/nearly
eins og = as/like
áður = before/earlier

Literal feel: “After an hour, feels to-him almost as before.”

Why is honum in the dative case (not hann)?

Because að líða in the “feel” sense is impersonal and takes a dative experiencer: the feeling “goes for” someone. So you say:

Mér líður vel. = I feel good. (to-me feels well)
Honum líður illa. = He feels bad. (to-him feels badly)

Can I say Hann líður to mean “He feels”?

Not for this meaning. For “feel (well/ill/etc.)” you must use the dative: Honum líður… / Henni líður… / Mér líður…
Note: Hann líður can occur in the separate meaning “he suffers” (rare/poetic), but to avoid ambiguity use Hann þjáist for “he suffers.”

What is the grammatical subject here?

There isn’t a normal nominative subject. Líður is used impersonally with a dative experiencer (honum). Think “It goes/feels for him.”

Why does the verb come before honum (i.e., líður honum)?

Icelandic is verb-second (V2) in main clauses. Since the time phrase Eftir klukkutíma is fronted, the finite verb must take the second slot:

Eftir klukkutíma líður honum…
If you don’t front the time phrase, you can say: Honum líður…

Does Eftir klukkutíma mean “in an hour” or “after an hour”?

Both ideas overlap here: it means that one hour later (from a reference point) he feels almost as before. In many contexts eftir + accusative with a time expression corresponds to English “in X (time from now)” or “after X (has passed).”

Why is klukkutíma in the accusative?

With this time-meaning, eftir governs the accusative. The noun klukkutími declines with accusative singular klukkutíma. (Fun fact: its dative singular is also klukkutíma, so the form looks the same, but here it’s accusative because of eftir.)

What’s the difference between klukkutími and klukkustund?

Both mean “an hour.” Klukkutími is very common in everyday speech; klukkustund can feel a bit more formal or written. Either is fine here:

Eftir klukkustund líður honum… (also correct)

What does næstum modify, and can I move it?

Næstum (“almost”) modifies the following comparison phrase eins og áður (“as before”). Typical placements:

Eftir klukkutíma líður honum næstum eins og áður.
Honum líður næstum eins og áður eftir klukkutíma. Keep it close to what it modifies to avoid ambiguity.

What exactly does eins og áður mean? When would I use áður en instead?

Eins og áður = “as/like before,” referring to an earlier state.
Use áður en to introduce a full clause: “before (someone does/did something),” e.g. áður en hann fór = before he went.

Could I say eins vel og áður?

Use jafn for “as … as” with adjectives/adverbs:

Honum líður næstum jafn vel og áður. = He feels almost as well as before.
Eins og is fine for general “as/like” comparisons, but equality with adjectives/adverbs typically uses jafn X og.

Are there natural word-order alternatives?

Yes:

Honum líður næstum eins og áður eftir klukkutíma.
Eftir eina klukkustund líður honum næstum eins og áður.
More explicit: Eftir klukkutíma líður honum næstum eins og hann gerði áður.

How is líður used when talking about time passing?

That’s the other core meaning of að líða: “to elapse/pass.” Examples:

Liðinn er klukkutími. = An hour has passed.
Dagurinn líður hægt. = The day passes slowly. In our sentence, it’s the “feel” meaning with a dative experiencer.

Any quick pronunciation tips?

líður: the í is long; ð is the voiced “th” in English “this.”
honum: the o is rounded (like British “lot”).
eins: “ayns”; og: roughly “oh”; áður: the á is like “ow” in “now,” and the ð is the voiced “th.”