Learn Hardcore Croatian: To je restoran koji je zatvoren danas. - That is the restaurant which is closed today.

To je restoran... = That/This is a restaurant... (very common introduction of a new thing).
On je restoran... would sound odd, because on means he; you normally use it for people or sometimes for clearly masculine nouns already known in the context, not to introduce a place.
Taj restoran je zatvoren danas = That restaurant is closed today.
Here the structure is different: Taj restoran is the subject, and you’re saying something about it.

So:

To je restoran koji je zatvoren danas. → Identifying: That is the restaurant that is closed today.
Taj restoran je zatvoren danas. → Describing a known restaurant: That restaurant is closed today.

Why is to neuter when restoran is masculine?

In structures like To je X, to is not agreeing in gender with X; it behaves like a fixed demonstrative pronoun meaning roughly this/that (thing).

You can think of it as:

To je restoran... ≈ That (thing) is a restaurant...

The gender agreement is shown on the noun restoran and any adjectives referring to it, not on to. This pattern is very common:

To je kuća. – That is a house. (kuća = feminine)
To je dijete. – That is a child. (dijete = neuter)
To je restoran. – That is a restaurant. (restoran = masculine)

In all of them, to stays neuter.

Could I also say Ovo je restoran koji je zatvoren danas or Taj je restoran koji je zatvoren danas? What is the difference from To je restoran...?

Yes, you can, but there are subtle differences in meaning and usage.

Ovo je restoran koji je zatvoren danas.
Ovo usually refers to something physically near the speaker: This is the restaurant that is closed today.
To je restoran koji je zatvoren danas.
To is neutral or can mean that, not necessarily very near or very far: That/This is the restaurant that is closed today.
Taj je restoran koji je zatvoren danas.
This is grammatically possible but stylistically unusual. More natural would be:
- Taj restoran je zatvoren danas. – That restaurant is closed today.
- or To je taj restoran koji je zatvoren danas. – That is the restaurant that is closed today.

So:

Use To je... as the default That is / This is pattern.
Use Ovo je... if you want to stress physical closeness (pointing at something right in front of you).
Use Taj restoran je... when the restaurant is already known and you are talking about it, not identifying it.

Why is the relative pronoun koji used here, and not koja or koje?

The relative pronoun koji must agree with its antecedent (restoran) in gender and number, and it takes its case from its role in the relative clause.

restoran is masculine singular.
In the relative clause koji je zatvoren danas, the relative pronoun is the subject of je zatvoren, so it is in the nominative case.

So we need:

nominative masculine singular form of koji → that is koji.

Other forms you mentioned:

koja: nominative feminine singular, or neuter plural
koje: can be nominative/accusative neuter singular, or genitive/dative/locative feminine singular, or nominative/accusative feminine plural (context decides)

Examples for contrast:

To je kuća koja je zatvorena danas. (kuća = feminine → koja)
To je mjesto koje je zatvoreno danas. (mjesto = neuter → koje)
To je restoran koji je zatvoren danas. (restoran = masculine → koji)

Can I drop koji je and just say To je restoran zatvoren danas, like English That is the restaurant closed today?

Not in the same simple way as in English. Croatian does not naturally drop the relative pronoun here.

To je restoran zatvoren danas sounds unnatural and calqued from English. You normally need the explicit relative clause:

To je restoran koji je danas zatvoren.

If you want to avoid koji je, you would normally change the structure:

To je danas zatvoreni restoran.
(That is a restaurant that is closed today. – literally That is a today-closed restaurant, with zatvoreni as an adjective before the noun.)

But if you want to stay as close as possible to the original structure and meaning, keep:

To je restoran koji je (danas) zatvoren.

Why is it zatvoren and not zatvoreni or zatvoreno in this sentence?

Here zatvoren is used as a predicative adjective / passive participle agreeing with restoran:

restoran – masculine singular
→ zatvoren – masculine singular form

So:

Restoran je zatvoren. – The restaurant is closed.
Kuća je zatvorena. – The house is closed. (feminine singular: zatvorena)
Mjesto je zatvoreno. – The place is closed. (neuter singular: zatvoreno)

Zatvoreni is usually the attributive (long) form used before a noun:

zatvoreni restoran – the closed restaurant
zatvorena kuća – the closed house

So:

To je restoran koji je zatvoren danas. – predicative: that is the restaurant that is closed today.
To je danas zatvoreni restoran. – attributive: that is the today-closed restaurant.

Is je zatvoren like English is closed or like has been closed? What tense/structure is this?

Je zatvoren is a combination of:

je – present tense of biti (to be)
zatvoren – passive participle / adjective

Functionally, this can express:

a state: is closed (the current condition)
sometimes the result of a previous action: has been closed (by someone, earlier)

Croatian here doesn’t strictly distinguish is closed vs has been closed the way English does. Context usually decides if you are emphasizing the present state or the prior action.

Examples:

Restoran je zatvoren danas. – The restaurant is closed today. (focus on state)
Restoran je jučer bio zatvoren. – The restaurant was closed yesterday. (bio zatvoren → past state)

Where can I put danas in this sentence? Is To je restoran koji je danas zatvoren better than ...koji je zatvoren danas?

Both are grammatically correct:

To je restoran koji je zatvoren danas.
To je restoran koji je danas zatvoren.

The main rule you must respect is the position of the clitic je: it must be in second position in its clause. In the relative clause koji je zatvoren danas, the first word is koji, so je must come immediately after it.

You can move danas relative to zatvoren, but not in front of je.

Nuance:

koji je danas zatvoren → slightly more natural; danas is close to the verb phrase.
koji je zatvoren danas → a bit more emphasis on danas at the end (stylistic).

If you say koji danas je zatvoren, that is incorrect, because it breaks the second-position rule for je.

How would I say That is the restaurant that was closed yesterday using the same pattern?

You typically show the past state with bio (past of biti) plus zatvoren:

To je restoran koji je jučer bio zatvoren.
Literally: That is the restaurant which yesterday was closed.

Structure:

To je restoran – That is the restaurant
koji – which (masculine singular, nominative, agreeing with restoran)
je bio zatvoren – was closed
jučer – yesterday (can go before bio or at the end: koji je bio zatvoren jučer)

So the safest, natural version:

To je restoran koji je jučer bio zatvoren.