Learn Hardcore Russian: На экране видно сообщение от сестры. - A message from my sister is visible on the screen.

For things shown by a display, Russian uses на + prepositional: на экра́не (“on the screen”). В экра́не would literally be “in the screen” and sounds wrong unless you mean physically inside the device or a hole in it.

What case is экра́не, and why does it end in -е?

It’s the prepositional singular of экра́н used after на for static location: экра́н → на экра́не. The prepositional singular of most masculine nouns ends in -е.

What is ви́дно here—verb, adjective, or something else?

Ви́дно is a predicative word meaning “is visible.” It doesn’t conjugate like a verb. Russian often uses it in impersonal-style sentences to state that something can be seen.

Why ви́дно and not ви́ден/видна́/видны́?

Both patterns exist:

With agreement (personal): the predicate agrees with the noun—ви́ден (m), видна́ (f), ви́дно (n), видны́ (pl). Example: На экра́не видна́ ико́нка.
Impersonal-style: ви́дно with no agreement. Example: На экра́не ви́дно сообще́ние. Your sentence is fine because сообще́ние is neuter singular, which matches ви́дно.

Is сообще́ние the subject or the object in this sentence?

In practice, it can be analyzed either way:

Subject analysis (agreeing predicate): (Что?) сообще́ние is the subject; ви́дно matches its neuter gender.
Impersonal analysis: ви́дно functions without a grammatical subject, and сообще́ние is what is seen. With inanimate neuter singular, the forms look identical, so both readings are acceptable.

Can I change the word order?

Yes. Common variants:

Сообще́ние от сестры́ ви́дно на экра́не.
На экра́не ви́дно сообще́ние от сестры́. Russian word order is flexible; fronting на экра́не highlights the location first.

What does от сестры́ mean, and why that ending?

От means “from (a person/source).” It takes the genitive case, so сестра́ → сестры́ (gen. sg.). Thus, от сестры́ = “from (my/his/her) sister.”

Could I say сообще́ние сестры́ instead of сообще́ние от сестры́?

You can, but the nuance differs:

Сообще́ние от сестры́ focuses on the sender (she sent it).
Сообще́ние сестры́ is a possessive-like “the sister’s message” (a message that belongs to/was written by her), and is less common in the context of incoming messages.

Do I need to add a possessive pronoun, like от мое́й сестры́?

Only if you need to specify whose sister. От сестры́ is context-dependent and can mean “from my/his/her sister.” To be explicit: от мое́й/твоей/его́/её сестры́.

How do I negate this naturally?

Use не ви́дно and (often) genitive for what isn’t visible:

На экра́не не ви́дно сообще́ния (от сестры́). The genitive after negation is preferred here.

Can I express the experiencer, like “to me it’s visible”?

Yes, with dative: Мне ви́дно сообще́ние (на экра́не). This is grammatical and means “I can see the message.” In everyday speech, Я ви́жу сообще́ние is often more direct/natural.

Does ви́дно ever mean “apparently”?

Yes, as a sentence adverb: Ви́дно, он за́нят. = “Apparently, he’s busy.” In your sentence, ви́дно clearly means “is visible,” not “apparently.”

How do I put this in the past or future?

Add the appropriate form of быть:

Past: Вчера́ на экра́не бы́ло ви́дно сообще́ние (от сестры́).
Future: За́втра на экра́не бу́дет ви́дно сообще́ние (от сестры́).

Are there synonyms that change the nuance?

Отобража́ется/показа́но: “is being displayed/is shown” (technical/formal).
Появи́лось: “appeared” (focus on the moment it showed up).
Замéтно: “noticeable” (not strictly visual clarity). Your sentence with ви́дно neutrally states visibility.

Where is the stress in the key words?

на экра́не (экра́н, экра́не)
ви́дно
сообще́ние
сестры́