Мама добавила удобрение в почву, и через неделю у орхидеи появился новый бутон.

Because Russian past-tense verbs agree with the subject in gender and number.

• мама is feminine singular
• so the verb is добавила

Compare:

• Мама добавила = Mom added
• Папа добавил = Dad added
• Родители добавили = The parents added

In the past tense, this gender marking is very common and important.

Удобрение is the direct object of добавила, so it is in the accusative case.

But here is the helpful part: for many inanimate neuter nouns, the accusative singular looks exactly like the nominative singular.

So:

• nominative: удобрение
• accusative: удобрение

That is why the form does not visibly change.

Because в can take different cases depending on the meaning:

• в + accusative = motion into / direction into
• в + prepositional = location in / inside

Here the idea is adding fertilizer into the soil, so Russian uses в + accusative:

• в почву = into the soil

Compare:

• удобрение в почву = fertilizer into the soil
• в почве = in the soil

So в почву is correct because there is a sense of putting something into it.

Через неделю means a week later or in a week, depending on context.

In this sentence, it means:

• a week later
• after a week

The preposition через is used with the accusative case to talk about time after some interval:

• через час = in an hour / an hour later
• через день = a day later
• через неделю = a week later

That is why неделя becomes неделю.

Yes, literally у often means something like by, near, or at, but in Russian it is also used in a very common structure meaning something exists/appears with someone or something.

So:

• у орхидеи появился новый бутон literally: at the orchid, a new bud appeared natural English: the orchid developed a new bud / a new bud appeared on the orchid

This is a very natural Russian way to express possession or appearance.

Compare:

• У меня есть книга = I have a book
• У дерева появились листья = Leaves appeared on the tree
• У орхидеи появился новый бутон = A new bud appeared on the orchid

Because у requires the genitive case.

The dictionary form is:

• орхидея = orchid

After у, it becomes genitive singular:

• у орхидеи = on the orchid / with the orchid / at the orchid

So the ending changes because of case, not because the meaning becomes plural.

The subject is новый бутон.

That is why the verb is появился:

• бутон is masculine singular
• so the past-tense verb is masculine singular: появился

Even though у орхидеи comes earlier in the sentence, it is not the subject. It is part of a prepositional phrase.

So the structure is roughly:

• у орхидеи = on the orchid
• появился = appeared
• новый бутон = a new bud

Because Russian word order is much more flexible than English word order.

In this kind of sentence, putting the verb before the subject often sounds natural when introducing something new:

• появился новый бутон = a new bud appeared

This word order helps present new information. It is a bit like saying, there appeared a new bud.

You could also say:

• У орхидеи новый бутон появился

but that has a different emphasis and is less neutral here.

So the original order is very natural for narration.

Both verbs describe completed, one-time events.

• добавила = added, completed the action
• появился = appeared, came into existence

Russian often uses the perfective aspect for events that move the story forward.

If you used imperfective forms, the meaning would change:

• добавляла = was adding / used to add
• появлялся = was appearing / used to appear

So the perfective forms fit the sentence because it tells a sequence of finished events.

A бутон is a bud — a flower that has not opened yet.

A цветок is a flower — usually an open flower, or sometimes the flower in a general sense.

So:

• новый бутон = a new bud
• новый цветок = a new flower

For an orchid, бутон suggests the plant is about to bloom, not that the flower is already open.

Because и is joining two separate clauses, each with its own grammatical base:

1. Мама добавила удобрение в почву
2. у орхидеи появился новый бутон

In Russian, when и connects two full clauses, a comma is usually needed.

But if и only joins two words or two parts of one clause, there is usually no comma.

Russian has no articles like a, an, and the.

So nouns such as мама, удобрение, почва, орхидея, and бутон do not show that distinction directly. English has to add it based on context.

In this sentence, natural English would usually be:

• Mom added fertilizer to the soil, and a week later the orchid developed a new bud.

But depending on context, you could also imagine:

• the fertilizer
• the soil
• an orchid
• the orchid

Russian leaves that to context, not grammar.