Ausländische Gäste kommen heute an.

Yes—adjectives are normally lowercase in German.

In this sentence, Ausländische is capitalized only because it is the first word of the sentence. If the same phrase appeared in the middle of a sentence, it would be:

... ausländische Gäste ...

By contrast, Gäste is capitalized because it is a noun, and all German nouns are capitalized.

Because it is an adjective describing Gäste, and German adjectives change their endings depending on case, number, and whether there is an article.

Here, ausländische Gäste is:

• plural
• nominative (the subject of the sentence)
• with no article

In that situation, the adjective takes the ending -e:

• ausländische Gäste

Compare:

• die ausländischen Gäste = the foreign guests
• ausländische Gäste = foreign guests

So the -e ending is part of normal adjective declension.

It is in the nominative case because it is the subject of the sentence—the people doing the action.

In Ausländische Gäste kommen heute an, the guests are the ones arriving, so ausländische Gäste is nominative plural.

Because the subject is plural: Gäste = guests.

German verbs change depending on the subject:

• der Gast kommt = the guest arrives
• die Gäste kommen = the guests arrive

So kommen is the correct present-tense form for they / plural.

Because the verb here is actually ankommen, not just kommen.

ankommen is a separable verb:

• infinitive: ankommen
• in a normal main clause: the prefix an- separates and moves to the end

So:

• Die Gäste kommen an. = The guests arrive.
• not Die Gäste ankommen.

This is a very common German pattern with separable-prefix verbs.

They are related, but not identical.

• kommen = to come
• ankommen = to arrive

So:

• Die Gäste kommen. can mean The guests are coming or The guests come
• Die Gäste kommen an. specifically means The guests arrive / are arriving

In this sentence, the idea is specifically arrival, so ankommen is the right verb.

German very often uses the present tense to talk about the future, especially when there is a time word like heute, morgen, bald, etc.

So:

• Ausländische Gäste kommen heute an.

naturally means something like:

• Foreign guests are arriving today
• or Foreign guests arrive today

German can use werden for the future, but it is often unnecessary if the time is already clear.

For example:

• Ausländische Gäste werden heute ankommen.

This is possible, but usually less natural in everyday speech than the simple present.

Yes, heute can move, but the verb still has to stay in the normal second position in a main clause.

The original sentence is:

• Ausländische Gäste kommen heute an.

You can also say:

• Heute kommen ausländische Gäste an.

Both are correct. The difference is mainly emphasis:

• starting with Ausländische Gäste puts focus first on the guests
• starting with Heute puts focus first on the time

What does not change in a main clause is this:

• the conjugated verb kommen stays in position 2
• the separable prefix an stays at the end

German plurals are not made in just one regular way, so you often have to learn the plural form with each noun.

For der Gast, the plural is:

• der Gast = the guest
• die Gäste = the guests

This plural uses:

• an umlaut: a → ä
• and the ending -e

Many German nouns change their vowel in the plural, but not all of them do.

ausländisch means foreign, usually in the sense of from another country.

So ausländische Gäste means guests from abroad / foreign guests.

It is not the same as international:

• ausländisch = foreign
• international = international

For example:

• ausländische Gäste = guests from other countries
• internationale Gäste = international guests

Those can overlap, but they are not always identical in meaning.

With a definite article, it would be:

• Die ausländischen Gäste kommen heute an. = The foreign guests are arriving today.

Notice how the adjective ending changes:

• ausländische Gäste
• die ausländischen Gäste

That happens because the article die already shows important grammatical information, so the adjective uses a different ending.

This is a very common pattern in German adjective declension.