Ярлык приложения исчез с экрана, и мне пришлось искать его через поисковую строку.

In this sentence, ярлык means an icon or shortcut, especially on a phone, tablet, or computer screen.

So ярлык приложения is:

• the app icon
• or the app shortcut

Although ярлык can also mean label or tag in other contexts, here it clearly means the clickable icon for an app.

Because приложения is in the genitive case.

Russian often uses this pattern to show possession or relationship:

• ярлык приложения = the app’s icon / the icon of the app
• страница книги = the page of the book
• ручка двери = the door handle

So the structure is:

• ярлык = icon
• приложения = of the app

The dictionary form is приложение, but after a noun like ярлык, Russian uses the genitive: приложения.

Экрана is genitive singular.

The preposition с can mean from, and when it shows movement away from somewhere, it takes the genitive:

• с экрана = from the screen
• со стола = from the table
• с полки = from the shelf

So:

• экран = screen
• с экрана = from the screen

The sentence is describing the icon as disappearing from the screen, so genitive is required.

Исчез means disappeared or vanished. It is a very natural choice here.

You could also hear пропал in similar situations:

• Ярлык исчез с экрана.
• Ярлык пропал с экрана.

Both can work, but there is a slight nuance:

• исчез focuses on the fact that it vanished
• пропал can sound a little more like went missing

In this sentence, исчез sounds neutral and standard.

This is a very common Russian structure.

мне пришлось comes from прийтись / приходиться, which often means:

• to have to
• to be forced to
• to end up needing to

So:

• мне пришлось искать = I had to search
• literally: it fell to me to search / it became necessary for me to search

Russian often uses the dative for the person affected in impersonal constructions:

• мне пришлось = I had to
• ему пришлось = he had to
• нам пришлось = we had to

This is why you see мне, not я.

Because искать focuses on the process of searching, not the successful result.

Compare:

• мне пришлось искать его = I had to look for it
• мне пришлось найти его = I had to find it
  This sounds less natural in this context, because find emphasizes the result.
• мне пришлось поискать его = I had to search for it for a while
  This is possible, but slightly different in nuance.

So искать is the most straightforward choice because the sentence is talking about the action the speaker had to do.

Его refers back to ярлык.

So:

• ярлык = icon
• искать его = search for it

Even though English uses it, Russian uses его because ярлык is a masculine noun.

Here его is the accusative form of the pronoun он:

• он = he / it
• его = him / it

For inanimate masculine nouns, Russian still uses его when replacing the noun with a pronoun.

It means through the search bar or using the search bar.

Here через does not mean literal physical movement. It often means by means of, via, or through a method:

• через приложение = through an app
• через интернет = through the internet
• через поисковую строку = through the search bar

So the speaker searched for the app icon by using the search bar.

It is accusative singular because the preposition через takes the accusative case.

The noun is:

• поисковая строка = search bar

After через, it becomes:

• через поисковую строку

Here is the breakdown:

• поисковая → поисковую
• строка → строку

Both words are feminine singular, so they change to match the accusative form.

Because и is joining two full clauses, each with its own grammatical center:

1. Ярлык приложения исчез с экрана
2. мне пришлось искать его через поисковую строку

Since these are two separate clauses, Russian normally puts a comma before и.

Very roughly:

• The app icon disappeared from the screen, and I had to search for it through the search bar.

Yes. Russian word order is flexible, though the emphasis changes.

The original version is neutral:

• Ярлык приложения исчез с экрана, и мне пришлось искать его через поисковую строку.

Other possible orders:

• С экрана исчез ярлык приложения...
  This puts more focus on from the screen
• Мне пришлось искать его через поисковую строку, потому что ярлык приложения исчез с экрана.
  This changes the sentence structure and emphasis

Russian word order often reflects what is already known and what is being emphasized, not just rigid grammar rules.

Yes. Поисковая строка is the normal way to say search bar or search field.

Depending on context, Russian speakers might also say things like:

• строка поиска
• поиск
• ввести в поиск = enter into search

But через поисковую строку is perfectly natural and clearly means using the search field on the device.

It could be either, but it most naturally suggests a phone or tablet home screen.

Why? Because ярлык приложения strongly suggests an app icon, and поисковая строка fits the idea of finding an app on a device.

Still, it could also work for a computer environment if the speaker is talking about an application shortcut on the screen.

So the sentence is not grammatically tied to one device, but the most likely everyday interpretation is a mobile device.