Learn Hardcore Korean: hotereseo chekeuaushagi jeone jidoreul hwaginhaeyo. - Before checking out of the hotel, I check the map.

체크아웃하기 전에 = “before checking out.”
Structure: [Verb stem] + 기 전에 + [main clause]. It tells you that the action in the main clause (checking the map) happens prior to the action in the dependent clause (checking out).

Why is 호텔에서 used instead of 호텔에 or no particle at all?

-에서 marks the location where an action takes place. Since you check out (and check the map) at the hotel:

호텔에서 = “at the hotel.”
Using 호텔에 would mark destination (“to the hotel”), and omitting a particle would be ungrammatical here.

Why is 체크아웃하기 used rather than 체크아웃을 하다?

Both are possible, but:

체크아웃하기 전에 uses a verbal noun form (verb stem + 기) to link directly with 전에.
체크아웃을 하기 전에 is also correct; here you nominalize with -을 하기 (“doing the checkout”) plus 전에.
Shorter form (체크아웃하기 전에) is more natural in spoken Korean.

What does 지도를 확인해요 literally mean, and why not use 보다 instead of 확인하다?

지도를 확인해요 literally means “(I) check/confirm the map.”
확인하다 implies verifying or confirming details (e.g., routes, landmarks).
보다 simply means “to look at.” If you just glance at the map, 봐요 works, but if you want to ensure you’re heading the right way, 확인해요 is more precise.

What tense and politeness level is 확인해요?

확인해요 is present tense, declarative.
It uses the -아요/어요 polite ending (also called 해요체), suitable for everyday conversation with strangers or acquaintances.

Could this sentence be said in a different word order?

Korean generally prefers the time/subordinate clause before the main clause, and the object before the verb. You might hear:

체크아웃하기 전에 호텔에서 지도를 확인해요. (The same elements, but moving 호텔에서 after the subordinate clause.)
All these word orders are grammatically correct, though the original order sounds smooth and natural.