Ebben az országban sok kerékpár van.

It breaks down like this:

• ebben = in this
• az = the
• országban = in country / in the country
• sok kerékpár = many bicycles
• van = there is / there are

So Hungarian is doing something very natural for itself, even if it looks a bit repetitive in English: it marks this and country in a way that ties them together.

A more word-for-word feel would be:

In-this the country-in many bicycle is

Natural English: There are many bicycles in this country.

Because Hungarian often marks the case on both the demonstrative and the noun phrase it belongs to.

Here:

• ez = this
• ebben = in this
• ország = country
• országban = in the country

So ebben az országban literally has in marked twice:

• once on this
• once on country

This is normal Hungarian grammar. When a demonstrative like ez (this) or az (that/the) goes with a noun, the case ending usually appears on the demonstrative too.

Other examples:

• ebben a házban = in this house
• abba a városba = into that city

Because ez and az are irregular when case endings are added.

So:

• ez
  • -ben becomes ebben
• az
  • -ban becomes abban

Not:

• ezben
• azban

This is just something you learn as a pattern:

• ez → ebben, ezt, ennek, etc.
• az → abban, azt, annak, etc.

So ebben is simply the correct inflected form of ez.

Because Hungarian commonly uses the pattern:

demonstrative + article + noun

So:

• ez a ház = this house
• az a könyv = that book
• ebben az országban = in this country

To an English speaker, the article may feel unnecessary, but in Hungarian it is the normal structure.

Also notice that the demonstrative and the noun phrase match in case:

• ebben = in this
• az országban = in the country

This is because of vowel harmony.

Hungarian suffixes often come in different versions. For the ending meaning in, the two main forms are:

• -ban
• -ben

Words with mostly back vowels usually take -ban:

• ország → országban

Words with mostly front vowels usually take -ben:

• szék → székben

But ebben is a fixed irregular form from ez, so you learn it as a whole form.

So in this sentence:

• ország has back vowels, so országban
• ebben is just the standard inflected form of ez

Because after numbers and quantity words like sok (many), Hungarian normally uses the noun in the singular.

So:

• egy kerékpár = one bicycle
• két kerékpár = two bicycles
• sok kerékpár = many bicycles

This is very different from English, where we say many bicycles with a plural noun.

In Hungarian, the quantity word already shows that there is more than one, so the noun usually stays singular.

Because sok kerékpár behaves like a quantified expression, and Hungarian commonly uses singular-style agreement here.

So:

• sok kerékpár van = there are many bicycles
• három ház van = there are three houses

This is normal Hungarian.

Compare that with a plain plural noun without a quantity word:

• Kerékpárok vannak az udvarban. = There are bicycles in the yard.

So with sok kerékpár, the singular van is expected.

That is a very common and important question.

Hungarian often drops van in the third person singular/plural present tense when it simply links a subject to a noun or adjective:

• A ház nagy. = The house is big.
• Ő tanár. = He/She is a teacher.

But in an existential sentence—when the meaning is there is / there are—Hungarian usually keeps van or vannak.

Here the sentence is existential:

• Ebben az országban sok kerékpár van.
• literally: In this country many bicycles exist.

So van is required.

Because quantified noun phrases like sok kerékpár usually do not take an article.

So Hungarian says:

• sok kerékpár = many bicycles
• not a sok kerékpár in this meaning

You can have a sok kerékpár, but then it usually means something more like the many bicycles or refers to a specific set already known in context, which is not what this sentence is doing.

Here it is just an indefinite quantity, so no article is used.

Yes, absolutely.

Both of these are natural:

• Ebben az országban sok kerékpár van.
• Sok kerékpár van ebben az országban.

The difference is mainly one of word order and emphasis.

• Ebben az országban... puts in this country first, setting the scene.
• Sok kerékpár van... starts with many bicycles, so that feels a bit more central.

Hungarian word order is flexible, but it is not random. It often reflects what is already known, what is being emphasized, or what the speaker wants to highlight.

Kerékpár is a correct standard word meaning bicycle.

In everyday speech, many people also say:

• bicikli

So:

• kerékpár = standard/formal-neutral
• bicikli = very common, everyday

Your sentence with kerékpár is completely natural and correct, especially in standard written Hungarian.