В этом музее можно увидеть старинные картины, а не только современные произведения искусства.

Because в can mean either in or into, depending on the case.

• в этом музее = in this museum → location, so Russian uses the prepositional case
• в этот музей = into this museum / to this museum → motion toward a place, so Russian uses the accusative case

Here the sentence is talking about what can be seen inside the museum, not movement toward it.

Because этот has to agree with музей in gender, number, and case.

• музей is masculine singular
• after в with the meaning of location, it is in the prepositional case
• so этот changes to its masculine singular prepositional form: этом

So:

• этот музей = this museum
• в этом музее = in this museum

Можно is an impersonal word meaning something like:

• it is possible
• one can
• you can

So можно увидеть means it is possible to see or more naturally you can see.

There is no specific subject like я, мы, or они. Russian often uses this kind of impersonal construction when talking generally.

Увидеть is the perfective form, while видеть is imperfective.

In this sentence, увидеть is natural because it focuses on the result: a visitor is able to see / catch sight of / encounter these things in the museum.

• можно увидеть = you can see / you can get to see
• можно видеть would sound more like it is possible to be seeing or would emphasize an ongoing/general visual experience

In descriptions of places, Russian very often uses можно + perfective infinitive to mean you can find / observe / see something there.

They are in the accusative case because they are the direct objects of увидеть.

However, for inanimate plural nouns, the accusative looks the same as the nominative. That is why these forms may look unchanged.

• старинные картины = accusative plural
• современные произведения искусства = accusative plural

Compare with animate nouns, where accusative plural would usually look like the genitive plural instead.

Because картина is an inanimate noun.

For most inanimate nouns in Russian:

• nominative plural = accusative plural

So:

• картины can mean paintings as a subject
• картины can also mean paintings as a direct object

The case is understood from the sentence structure.

This is an important vocabulary distinction.

• старые = simply old
• старинные = antique, old-time, historical, often with a sense of age and cultural value

So старинные картины suggests antique/old master paintings or at least paintings from an earlier period, not just paintings that happen to be old or worn out.

Because искусства here is genitive singular and forms a common phrase:

• произведение искусства = a work of art
• произведения искусства = works of art

Russian often uses this pattern: a main noun + another noun in the genitive to specify what kind of thing it is.

So искусства here means of art, not a plural arts.

Here а introduces a contrast, and не только means not only / not just.

The idea is:

• you can see antique paintings
• not just modern works of art

So а не только gives a contrast like:

• rather than only
• and not just
• not only ... but also, though in this sentence the structure is shortened

A fuller rewording could be:

В этом музее можно увидеть не только современные произведения искусства, но и старинные картины.

That version starts with not only modern works of art, but also antique paintings. The original sentence flips the order for emphasis.

Because а is a coordinating conjunction, and in Russian it is normally preceded by a comma when it connects two contrasting parts.

Here it links:

• старинные картины
• а не только современные произведения искусства

The comma helps mark the contrast clearly.

Yes. Russian word order is flexible, and changing it changes the focus or emphasis, not the basic meaning.

For example:

• В этом музее можно увидеть старинные картины, а не только современные произведения искусства.
  Focuses first on the interesting fact that antique paintings are there.

• В этом музее можно увидеть не только современные произведения искусства, но и старинные картины.
  A more balanced not only ... but also structure.

• Старинные картины можно увидеть в этом музее...
  Emphasizes старинные картины

So the original is natural, but not the only possible order.

Because Russian has no articles.

English needs words like the and a/an, but Russian usually expresses that meaning through context, word order, and sometimes demonstratives like этот (this).

So:

• музей can mean a museum or the museum, depending on context
• этот музей specifically means this museum

In this sentence, этом already makes the noun specific: in this museum.