Learn Polish: Nauczyciel oprowadza tych turystów po muzeum. - The teacher is showing these tourists around the museum.

The preposition po followed by the Locative case is used for movement 'around' or 'all over' a surface or area. While w muzeum just tells us where they are ('in the museum'), po muzeum emphasizes the action of walking around from place to place inside it.

Why doesn't the noun muzeum change its ending after po?

The preposition po requires the Locative case here, but neuter nouns borrowed from Latin that end in -um (like muzeum or centrum) are indeclinable in the singular. This means they keep their dictionary form in all singular cases.

Why is 'these tourists' translated as tych turystów if it's the direct object?

As the direct object, it takes the Accusative case. However, for masculine personal nouns in the plural (groups including at least one man), the Accusative case is identical to the Genitive case. So we use the Genitive forms tych and turystów.

Is the verb oprowadza related to prowadzić (to lead)?

Yes! Polish often creates new meanings by adding prefixes to base verbs. The base verb prowadzić means 'to lead' or 'to guide'. Adding the prefix o- (which often gives a sense of going 'around') creates oprowadzać, meaning 'to lead around' or 'to show around'.