Призрак появился в старом доме.

The dictionary form is появиться.

That verb is:

• perfective
• roughly to appear, to show up, to come into view

So появился is the past-tense form used with a masculine singular subject.

In Russian, the past tense agrees with the subject in gender and number.

Here the subject is призрак, which is a masculine singular noun, so the verb is появился.

Compare:

• призрак появился — masculine
• тень появилась — feminine
• существо появилось — neuter
• призраки появились — plural

This is a question of aspect.

• появился is perfective: it presents the appearance as a single completed event
• появлялся is imperfective: it suggests repeated appearance, habitual action, or focus on the process

So in this sentence, появился means the ghost appeared at some moment.
If you said появлялся, it could mean something like used to appear or was appearing depending on context.

Because this sentence describes location, not movement into a place.

With в:

• в + prepositional case = in / inside a place
• в + accusative case = into a place

So:

• в старом доме = in the old house
• в старый дом = into the old house

Here the ghost appears in the house, so Russian uses the prepositional case.

Because after в in a location meaning, the noun phrase goes into the prepositional case.

Base forms:

• старый → старом
• дом → доме

The adjective must agree with the noun in:

• case
• number
• gender

So both words change together:

• nominative: старый дом
• prepositional: в старом доме

Призрак is in the nominative case, because it is the subject of the sentence.

It is the thing doing the action of appearing.

So the basic structure is:

• Призрак — subject
• появился — verb
• в старом доме — location

Yes. Russian word order is flexible.

You can say:

• Призрак появился в старом доме
• В старом доме появился призрак

Both are correct, but the emphasis changes a little.

A common tendency:

• Призрак появился в старом доме — starts with the ghost
• В старом доме появился призрак — starts with the location, which can sound more atmospheric or narrative

Russian often uses word order to show focus or what information is new.

Russian has no articles.

So призрак can mean:

• a ghost
• the ghost

And в старом доме can mean:

• in an old house
• in the old house

Context tells you which one is meant.

This is very normal in Russian, so learners have to get used to understanding definiteness from context rather than from separate words.

They are not the same.

• Призрак появился в старом доме = the ghost appeared there, showed up there, became visible/present there
• Призрак был в старом доме = the ghost was in the old house

So появился focuses on the moment of appearing.
Был only states presence.

The stress is:

При́зрак появи́лся в ста́ром до́ме.

A rough pronunciation guide:

• При́зрак → PREE-zrak
• появи́лся → pəyə-VEEL-sya
• в ста́ром → f STA-rəm
• до́ме → DO-mye

A few useful notes:

• в is often pronounced like f before a voiceless consonant
• the stress in появи́лся is on ви
• unstressed vowels are reduced in normal speech

Usually yes. В strongly suggests inside the house.

If you want near/by the old house, Russian would more naturally use:

• у старого дома

So:

• в старом доме = in the old house
• у старого дома = by the old house / near the old house

That is an important distinction in Russian.