Quam laeta est caterva: quotiens mimus gesticulatur, totiens omnes rident!

Here quam is an exclamatory adverb, meaning how:

• Quam laeta est caterva! = How happy the crowd is!

It is not the relative quam meaning whom/which.
A good clue is that it comes directly before an adjective, laeta. With adjectives and adverbs, quam often introduces an exclamation.

Because laeta is a predicate adjective with est, so it must be in the nominative to agree with the subject caterva.

• caterva = nominative singular
• laeta = nominative singular feminine

Latin uses the nominative for both the subject and the adjective linked to it by to be:

• caterva est laeta = the crowd is happy

If it were laetam, that would be accusative, which would not fit here.

Caterva is nominative singular and is the subject of est.

So the structure is:

• caterva = the crowd / the group
• est = is
• laeta = happy

Together: the crowd is happy.

Even though a crowd contains many people, Latin treats caterva as a singular noun, just as English often does with crowd.

Latin word order is much freer than English word order. The sentence begins with Quam laeta to emphasize the exclamation:

• Quam laeta... = How happy...

Putting those words first makes the emotional tone strong right away.
A more neutral order such as Caterva quam laeta est would be much less natural.

So this is mostly about emphasis and style, not a change in basic meaning.

They are a correlative pair:

• quotiens = as often as / whenever
• totiens = so often / that often

So:

• quotiens mimus gesticulatur, totiens omnes rident

literally means:

• as often as the mime gestures, so often all laugh

In smoother English, you might say:

• whenever the mime gestures, everyone laughs
• every time the mime gestures, everyone laughs

This is a very common Latin pattern.

Yes. Gesticulatur is from a deponent verb.

A deponent verb:

• has passive forms
• but active meaning

So gesticulatur looks like a passive form because of the -tur ending, but it means:

• he gestures
• he makes gestures

Its dictionary form is gesticulor, gesticulari.

Mimus is the subject of gesticulatur, so it is nominative singular.

It means something like:

• mime
• comic performer
• actor in a mime show

It does not have to mean the modern idea of a silent, white-faced street performer. In Roman culture, a mimus was a stage entertainer, often in comic performance.

Here omnes is being used substantively, meaning the noun is understood:

• omnes = all (the people) / everyone

It is the subject of rident, so it is nominative plural.

Latin often uses adjectives this way, without an expressed noun, when the meaning is clear.

So:

• omnes rident = everyone laughs / all laugh

Because its subject, omnes, is plural.

• omnes = all, everyone
• rident = they laugh

So the verb must be third person plural.

This is a good example of checking agreement carefully: even though the earlier noun caterva is singular, that belongs to the first clause. In the second clause, the subject is omnes, not caterva.

They can suggest a vivid present scene, but the quotiens ... totiens pattern especially gives a sense of repeated action or habit:

• Whenever the mime gestures, everyone laughs

So the present tense here is best understood as something like:

• a lively description of what is happening
• and/or a general pattern in the scene

Latin present tense often does both very naturally.

The colon helps divide the sentence into two parts:

1. Quam laeta est caterva — an exclamation
2. quotiens mimus gesticulatur, totiens omnes rident — the reason or explanation

So the sense is roughly:

• How happy the crowd is: whenever the mime gestures, everyone laughs!

It is worth remembering that punctuation in printed Latin is largely an editorial aid. The grammar is doing the real work, but the colon helps modern readers see the connection quickly.