Learn Hardcore Swedish: Hans ansikte blir rött när någon säger att han är snygg. - His face turns red when someone says that he is good-looking.

Bli in Swedish expresses a change of state: to become / to get.
So Hans ansikte blir rött literally means “His face becomes red”, i.e. it turns red.

If you said Hans ansikte är rött, that would mean “His face is red” (describing a static situation), not that it turns red when something happens.
So blir is used because the redness appears as a reaction to what someone says.

Why is it rött and not röd?

Adjectives in Swedish agree with the gender and number of the noun.

ansikte is an ett-word: ett ansikte (a face)
With ett nouns in singular indefinite, the base form röd becomes rött

So:

ett rött ansikte – a red face
ett rött hus – a red house
en röd bok – a red book

That’s why it must be rött with ansikte.

Is Hans here the name “Hans”, or the pronoun “his”? How do I know?

In this sentence, Hans is almost certainly the possessive pronoun “his”, not the male name Hans.

Clues:

As a pronoun, hans is normally written with a lowercase h, but here it appears at the start of the sentence, where the first letter is capitalized anyway.
The structure hans ansikte (“his face”) is very common and natural.
If it were the name Hans, the sentence would mean “Hans’s face becomes red …”, which is possible but usually you’d show possession differently: Hans ansikte blir rött can indeed mean “Hans’s face becomes red”, but context would have to make that clear.

So grammatically, the written form is ambiguous, but in practice learners are usually meant to read this as “His face becomes red …” (the pronoun).

Why is it när and not om for “when”?

Both när and om can translate to “when” in English, but they’re used differently:

när = when (every time / at the time that)
- Hans ansikte blir rött när någon säger …
  → This is a real, recurring situation: Whenever someone says he is handsome, his face turns red.
om = mainly if / whether
- Hans ansikte blir rött om någon säger …
  → This sounds more hypothetical: His face would turn red if someone said…

So när is best here, because we are talking about something that actually happens regularly.

Why is the word order när någon säger (subject before verb) and not när säger någon?

In Swedish, subordinate clauses (introduced by när, att, eftersom, etc.) keep normal statement word order: subject → verb.

Main clause question: När säger någon det? – When does someone say that? (question word → verb → subject)
Subordinate clause: … när någon säger det. – … when someone says it. (subject → verb)

In your sentence, när någon säger att … is a subordinate clause, so the correct order is någon säger, not säger någon.

What is the function of att in när någon säger att han är snygg? Could we leave it out?

att here is a subordinating conjunction that introduces a content clause (what is being said):

någon säger att han är snygg
= someone says that he is handsome

In Swedish, att is normally required in this type of clause after verbs like säga, tro, tycka, veta, etc.
You generally cannot drop it the way you sometimes drop “that” in English.

So när någon säger han är snygg is ungrammatical; you need att.

Why is it han and not honom after att?

han is the subject form (nominative), while honom is the object form.
In att han är snygg, han is the subject of the verb är (he is handsome), so the subject form is required:

att han är snygg – that he is handsome
någon säger till honom – someone says to him (here honom is an object after a preposition)

So after att, you choose han or honom depending on the role inside that clause. Here the role is subject, so han is correct.

Who does han refer to here? Is it clearly the same person as hans?

Grammatically, han could refer either to:

The owner of the face (hans), or
Some other male person that “someone” is talking about.

Context usually makes this clear.
In most natural readings of this sentence used in learning materials, han refers to the same person as hans:

His face turns red when someone says that *he (that same person) is handsome.*

But Swedish, like English, can be ambiguous with pronouns; you sometimes have to rely on context or rephrase if it’s confusing.

What nuance does snygg have? Is it always about physical appearance?

snygg most often means “good-looking / attractive” about people, usually physically:

han är snygg – he is handsome
hon är snygg – she is attractive

It can also mean “nice-looking / neat” for things:

en snygg tröja – a nice(-looking) sweater
ett snyggt rum – a neat, tidy room

Compared to other words:

vacker – beautiful (a bit more poetic/formal)
söt – cute / sweet (often younger people, small animals, etc.)

So here snygg is natural: someone says that he is good-looking / handsome.

Could you also say Hans ansikte rodnar instead of blir rött? What’s the difference?

Yes, you can say Hans ansikte rodnar när …, and it’s perfectly correct.

bli röd / bli rött – become red, a more neutral, descriptive expression of the color change.
rodna – to blush, focuses more on the emotional reaction (embarrassment, shyness) causing the red face.

So Hans ansikte rodnar när någon säger att han är snygg sounds a bit more vivid and emotional than blir rött, which is more literal and physical.

Why is it när någon säger att han är snygg and not something like när någon säger till honom att han är snygg?

Both versions are possible, but they mean slightly different things:

när någon säger att han är snygg
→ when someone says that he is handsome (to anyone: to him, to others, in general)
när någon säger till honom att han är snygg
→ when someone tells him that he is handsome (specifically to him)

So the given sentence is more general; it doesn’t specify who hears the comment.
If you want to stress that the compliment is addressed directly to him, add till honom.

How would I make this sentence negative? Where does inte go?

Negation inte goes in different places in main vs subordinate clauses.

Negating the main clause (his face does not turn red):
- Hans ansikte blir inte rött när någon säger att han är snygg.
  → His face does not become red when someone says he is handsome.
Negating what is said (someone says that he is not handsome):
- Hans ansikte blir rött när någon säger att han inte är snygg.
  → His face becomes red when someone says that he is not handsome.

Note that in the subordinate clause att han är snygg, inte comes after the subject han and before the verb är: att han inte är snygg.