У одного цветка бутон ещё закрыт, а у другого уже видно белые лепестки.

Because у + genitive here means something like as for / with / on the case of that flower. It is very natural in Russian when talking about a feature or part belonging to something:

• У цветка бутон закрыт = The flower’s bud is closed / On the flower, the bud is closed

If you said на одном цветке, that would sound more spatial and literal: on one flower. That works when something is physically located on the flower. But here Russian prefers у because the bud and petals are being described as parts/features of the flower.

Because the preposition у requires the genitive.

So:

• цветок → цветка
• один → одного

That is why you get у одного цветка.

Because цветка is omitted as understood from the first half.

So the full underlying structure is:

• У одного цветка бутон ещё закрыт, а у другого цветка уже видно белые лепестки.

Russian often drops repeated words when the meaning is obvious. English does the same:

• one flower ... the other

Here it means the other one.

In the pattern у одного ..., а у другого ..., Russian is contrasting two items:

• one ... the other ...

So другой does not mainly mean different here; it means another/the other in a pairwise contrast.

Because бутон is the subject of the first clause.

The structure is:

• бутон ещё закрыт = the bud is still closed

So:

• бутон = subject, nominative
• закрыт = predicate

The phrase у одного цветка just gives the frame: as for one flower / on one flower.

Because закрыт is the short form, which is commonly used in predicates:

• Бутон закрыт. = The bud is closed.

By contrast, закрытый is the full form, usually used before a noun:

• закрытый бутон = a closed bud

So:

• закрытый бутон = adjective modifying a noun
• бутон закрыт = predicate statement

They create a time/contrast relationship:

• ещё = still
• уже = already

So the sentence contrasts two stages:

• one flower’s bud is still closed
• the other flower already shows white petals

This makes the comparison much clearer and more natural.

Because а marks a contrast or comparison.

Here the sentence is not just adding information; it is comparing two flowers:

• one flower is at one stage
• the other is at a later stage

So а is better than и because it means something like:

• while
• whereas
• but

Видно is an impersonal predicate meaning:

• it is visible
• you can see
• can be seen

So:

• у другого уже видно белые лепестки literally feels like with the other one, it is already possible to see white petals

This is a very common Russian way to talk about visibility without making a normal personal subject.

Because this sentence uses an impersonal construction.

• видно = it is visible / one can see
• видны = plural form agreeing with лепестки

So Russian has two possible ways to say something similar:

• У другого уже видно белые лепестки.
• У другого уже видны белые лепестки.

The first is impersonal and focuses on the fact that the petals can now be seen. The second makes лепестки the grammatical subject: the white petals are already visible.

Both are possible, but видно is very natural here.

It is best understood here as accusative plural, the object of видно.

But for inanimate plural nouns, the accusative and nominative look the same:

• nominative plural: белые лепестки
• accusative plural: белые лепестки

So the form does not change, which is why it can be confusing.

Compare with a singular example where the case is clearer:

• Видно белый лепесток / Видно белые лепестки
• С горы видно реку = You can see the river from the hill

Yes. Russian word order is flexible, though different orders change emphasis.

For example, you could also say:

• У одного цветка бутон ещё закрыт, а у другого уже видны белые лепестки.
• Бутон у одного цветка ещё закрыт, а у другого уже видно белые лепестки.

The original order is natural because it sets up a neat contrast:

• у одного ...
• а у другого ...

That makes the comparison easy to follow.