Katson karttaa, jotta löydän reitin museoon.

Katson is the 1st person singular present tense of katsoa (to look (at)).

• base verb: katsoa
• present 1st singular ending: -n So: katso- + -n → katson.

karttaa is the partitive singular of kartta (map). With verbs like katsoa (to look at), the object is typically in the partitive because it’s an ongoing/at-object activity rather than a “completed result”:

• Katson karttaa = I’m looking at a map (process, not “finishing” the map). Compare:
• Näen kartan = I see the map (more like a completed/whole perception).

jotta introduces a purpose clause: “so that / in order that”.
So the structure is:

• main clause: Katson karttaa,
• purpose clause: jotta löydän reitin museoon.

Finnish commonly uses the present indicative after jotta even when English would use can/will/would:

• jotta löydän = so that I (can) find / so that I will find
  Context supplies the “ability/future-ish” nuance; Finnish doesn’t require an extra modal here.

reitin is the total object form (formally genitive singular, but functioning as accusative for a 1st person subject). With löytää (to find), the result is typically a completed “found it” event, so Finnish uses a total object:

• löydän reitin = I find the route (a complete result) If it were negative or incomplete/indefinite, you’d often see the partitive:
• en löydä reittiä = I don’t find a route

Form-wise, reitin looks like the genitive singular. Function-wise, in this sentence it’s the accusative (total object). In Finnish grammar materials you’ll see both explanations:

• “genitive object” (common in learner contexts)
• “accusative/total object” (more functional description) Practically: reitin here signals a complete, bounded object of finding.

museoon is the illative case of museo, meaning into the museum / to the inside of the museum. Illative answers “where to (inside)?”:

• museoon = into/to the museum (inside)

Yes, but it changes the nuance:

• museoon (illative) = into the museum (inside)
• museolle (allative) = to the museum (often to the area/building, less explicit about going inside) With reitti, both can occur depending on whether you mean a route into the building or to the destination generally.

The given order is very natural. Finnish word order is somewhat flexible, but changes usually add emphasis:

• neutral: Katson karttaa, jotta löydän reitin museoon.
• emphasizing purpose/result: Jotta löydän reitin museoon, katson karttaa.
• emphasizing “the map”: Karttaa katson, jotta löydän reitin museoon. (more marked/stylized)

Yes. A common alternative is the -kse- purpose structure:

• Katson karttaa löytääkseni reitin museoon. = I look at the map to find the route to the museum.
  This is more compact than a jotta clause, and both are correct; choice depends on style and complexity of the clause.