Annuler cet événement rendrait Marie triste, alors ils se montrent prudents.

Because annuler is being used as an infinitive, meaning to cancel. In French, an infinitive can act like a noun or a whole action idea, just like English Canceling this event would make Marie sad or To cancel this event would make Marie sad.

So in:

Annuler cet événement rendrait Marie triste

the whole phrase annuler cet événement is the subject of the sentence.

Rendrait is the conditional present of rendre. It means would make.

• rend = makes
• rendra = will make
• rendrait = would make

Here, the speaker is talking about a hypothetical situation:

Canceling this event would make Marie sad

So the conditional is the natural choice.

Rendre + someone + adjective means to make someone + adjective.

Examples:

• rendre Marie triste = to make Marie sad
• rendre Paul heureux = to make Paul happy
• rendre la situation difficile = to make the situation difficult

So:

Annuler cet événement rendrait Marie triste
literally = To cancel this event would make Marie sad

French uses cet instead of ce before a masculine singular noun that starts with a vowel or mute h.

• ce livre = this book
• ce garçon = this boy
• cet événement = this event
• cet homme = this man

This is mainly for pronunciation: ce événement would sound awkward, so French uses cet.

Here, alors means something like so, therefore, or in that case.

In this sentence:

Annuler cet événement rendrait Marie triste, alors ils se montrent prudents.

it connects the two ideas:

1. Canceling the event would make Marie sad.
2. So they are being cautious.

It is showing a consequence or logical result.

Both are possible, but they are not exactly the same.

• ils sont prudents = they are cautious/prudent
  This describes their general state or quality.
• ils se montrent prudents = they show themselves to be cautious / they are acting cautiously
  This emphasizes how they are behaving or presenting themselves in this situation.

So se montrer often suggests demonstrating or showing a quality, not just possessing it.

The verb here is se montrer, which literally means to show oneself, but in practice often means to appear, to act, or to show oneself as something.

So:

• il se montre gentil = he is acting kindly / he shows himself to be kind
• ils se montrent prudents = they are behaving cautiously

The se is just part of the verb in this use.

Because prudents agrees with ils, which is plural.

French adjectives usually agree in gender and number with the noun or pronoun they describe:

• il se montre prudent
• elle se montre prudente
• ils se montrent prudents
• elles se montrent prudentes

Since ils is masculine plural (or mixed-gender plural), the adjective is prudents.

Grammatically, ils means they, but the sentence by itself does not tell us exactly who they are. It must come from the wider context.

That is very normal in French, just like in English. If the previous sentence mentioned a group of organizers, friends, or family members, ils would refer to them.

So this is not a special French grammar issue; it is just normal pronoun reference.

No, not in this structure.

With rendre meaning to make someone something/adjective, the person is usually the direct object:

• rendre Marie triste
• rendre les enfants heureux

Not:

• rendre à Marie triste

So Marie comes directly after the verb as the person affected.

French does not need an extra word here. The infinitive phrase itself works as the subject:

Annuler cet événement rendrait Marie triste

English can also do this:

• To cancel this event would make Marie sad

So French is simply using the infinitive directly, without adding anything like le fait de.

That said, French could also say:

Le fait d'annuler cet événement rendrait Marie triste

This is a little heavier and more explicit: The fact of canceling this event would make Marie sad.

Yes, in this pattern it comes after the direct object:

rendre + person + adjective

So:

• rendre Marie triste
• rendre Paul furieux
• rendre les élèves nerveux

That word order is standard. The adjective describes the state the person would be put into.

Yes, it is grammatically natural. It means something like:

Canceling this event would make Marie sad, so they are being cautious.

A native speaker might also choose slightly different wording depending on style, for example:

• Annuler cet événement rendrait Marie triste, alors ils font attention.
• Comme annuler cet événement rendrait Marie triste, ils se montrent prudents.
• Annuler cet événement attristerait Marie, alors ils se montrent prudents.

But the original sentence is correct and natural.