Unser Besuch ist schon da.

Because Besuch is a masculine singular noun in the nominative case here, and unser has to match it.

A quick comparison:

• unser Besuch = our visit / our visitor(s)
• unsere Familie = our family
• unsere Freunde = our friends

So the ending depends on the gender, number, and case of the noun, not on who owns it.

German grammar follows the grammatical form of the noun, not necessarily the real-world number of people involved.

Besuch is grammatically singular, so the verb is singular too:

• Unser Besuch ist da.

Even if Besuch means something like our guests or the people visiting us, the noun itself is still singular, so ist is correct.

It can mean either depending on context, which is something that often confuses learners.

Common meanings of Besuch:

• a visit
• visitor(s) / company / guests

In a sentence like Unser Besuch ist schon da, it usually means the people who are visiting us have arrived.

So this is one of those German nouns whose exact meaning depends on the situation.

Here schon means already.

It shows that something has happened earlier than expected, or that the speaker is noting that it has happened by now.

Examples:

• Er ist schon hier. = He is already here.
• Wir sind schon fertig. = We are already finished.

So schon adds the idea of already rather than just stating presence.

In this sentence, da means something like here or present.

German da can mean:

• there
• here
• present / available / arrived, depending on context

In ist schon da, it usually means:

• has arrived
• is here now

So although da often literally translates as there, in this kind of sentence English normally says here.

Because a possessive determiner like unser usually takes the place of an article.

So German normally says:

• unser Besuch
• mein Bruder
• ihre Katze

Not:

• der unser Besuch

This works much like English:

• our guest not
• the our guest

This is a normal German main clause, and German main clauses usually follow the verb-second rule.

That means:

• one element comes first
• the conjugated verb comes second

Here:

1. Unser Besuch
2. ist
3. schon da

You could also move another element to the first position for emphasis:

• Schon ist unser Besuch da.
  This is possible, but less neutral and more stylistic.

The original sentence is the most natural, neutral version.

Yes. Bereits is a good alternative to schon.

Difference in tone:

• schon = more common and conversational
• bereits = a bit more formal or written

So both are correct:

• Unser Besuch ist schon da.
• Unser Besuch ist bereits da.

In everyday speech, schon is usually the more natural choice.

Yes, but the nuance is slightly different.

• ist da often means has arrived / is present
• ist hier focuses more on location: the person is here

So:

• Unser Besuch ist schon da = Our visitors have already arrived / are already here.
• Unser Besuch ist hier = Our visitors are here.

Both can work, but da is especially common when talking about arrival or presence.

Because all German nouns are capitalized.

So:

• Besuch = noun, capitalized
• schon = adverb, not capitalized
• da = adverb, not capitalized

This is a general rule in German, not something special about this sentence.