Are collective nouns taught at school (and one has to learn them) or are they just a fun thing?

I speak English as a foreign language and find it unique in several aspects. One of them is the large number of collective nouns, especially for groups of birds. Such high degree of specificity reaches the point where you have several nouns for a single species, just depending on whether the group is on land, flying together, or just flying at random. We say there is a parliament of owls, a murder of crows, a company of parrots, a plump or moorhens, a clutch of chickens, a kettle of hawks, a watch of nightingales, a covey of partridges, a pod of pelicans, a sedge of cranes, a flock of geese on land, a plump of geese flying close, a skein of geese in flight, and so on. The list is indeed very long. My question is – Are these nouns standard in every English Speaking Country ? Are they treated seriously so native speakers have to learn them at school ? Or is it just a fun thing ? Can these collective nouns take both a singular and a plural verb - depending on context ?

Collective nouns in English are very often the stuff of trivia questions. This is due to their rarity in common usage.

There are several that are commonly used, though:

Pride of lions
Flock of sheep
Gaggle of geese
School of fish, etc.

Some are of moderate familiarity but rarely used (except in scientific or poetic use):

Murder of crows
Pod of whales

Some are never used outside trivia contest:

Clowder of cats
Kettle of hawks
Convocation of eagles
And, numerous other obscure collectives.

In general, these terms are seldom used, and are often quite antiquated. Most do not learn them in schools (except as interesting tidbits).

Here is a fairly extensive listing of animal collective nouns.

Groups of animals are more likely to be referred to as herds, flocks, or even merely groups.

As to whether or not they can be used with verbs: yes. Typically they take a singular verb form.

The pride runs quickly and quietly when it is on the hunt.

Are they treated seriously so native speakers have to learn them at school? Or is it just a fun thing?

From the Collective nouns Wikipedia page cited by David M

... the list in the Book of Saint Albans (1486) runs to 165 items, many of which, even though introduced by the compaynys of beestys and fowlys, do not relate to venery [words for groups of animals] but to human groups and professions and are clearly humorous.

Are these nouns standard in every English Speaking Country?

No. Looking at Wikipedia's List of animal names, we can see the reasonably standard generic collective nouns, such as pack of dogs, and the simply humorous, such as a bloat of hippopotamuses.