Der Hausmeister kommt vorbei und schaut sich den Rauchmelder in meiner Küche an.

vorbeikommen is a common verb meaning to come by / drop by / come over briefly.
In the sentence, Der Hausmeister kommt vorbei implies the caretaker is making a short visit (often to check or fix something), not “passing by without stopping.”

It’s one sentence with two actions joined by und:

• (Er) kommt vorbei
• (Er) schaut ... an
  German often omits repeating the subject (der Hausmeister) after und, just like English: “The caretaker comes by and looks at …”

sich etwas ansehen is a fixed expression meaning to look at / inspect / take a look at something (often carefully).
The sich is a reflexive pronoun that’s part of the idiom. In this context it suggests inspection rather than a quick glance.

anschauen is a separable verb (an- + schauen).
In a normal main clause, the prefix goes to the end:

• Er schaut sich den Rauchmelder an.
  In an infinitive/“to”-form it stays together:
• Er will sich den Rauchmelder anschauen.

Because den Rauchmelder is the direct object (accusative).
Rauchmelder is masculine (der Rauchmelder in nominative), and masculine accusative changes der → den.

Here in describes a location (not movement), so it takes the dative: in + dative.
Küche is feminine (die Küche), so dative is der Küche. The possessive matches that:

• in meiner Küche (dative feminine)

With two-way prepositions like in, the rule is:

• Where? (location) → dative
• Where to? (movement/destination) → accusative

Here, the smoke detector is already in the kitchen and he’s inspecting it there → location → dative (in meiner Küche).
If it were movement: Er geht in meine Küche = “He goes into my kitchen” (accusative).

It often implies checking/inspecting rather than just “looking.” In everyday German, sich etwas anschauen / ansehen can mean anything from “have a look” to “inspect,” and with something like a Rauchmelder it strongly suggests an inspection (e.g., functionality, battery, placement).

Hausmeister can cover several roles depending on the building: caretaker, building superintendent, janitor, sometimes maintenance person. In apartment buildings, it often means someone who handles repairs, checks equipment, coordinates contractors, etc.

Yes, you can move it, but the given order is very natural. Common options include:

• ... schaut sich den Rauchmelder in meiner Küche an. (focus on which smoke detector)
• ... schaut sich in meiner Küche den Rauchmelder an. (focus slightly more on the location)
• ... schaut sich den Rauchmelder an, in meiner Küche. (more like an afterthought/added detail)

In the original, in meiner Küche sits next to den Rauchmelder because it specifies which smoke detector (the one located in the kitchen).