jidoreul bomyeonseo gireul hwaginhaeyo.

If the verb stem ends in a consonant, you add -으면서. If it ends in a vowel, you add -면서.
• 보다 → 보 + 면서 → 보면서
• 먹다 → 먹 + 으면서 → 먹으면서

Yes, -고 connects actions too, but it usually just lists them or implies sequence.
• 지도를 보고 길을 확인해요 can mean “I look at the map and then check the route.”
By contrast, 보면서 emphasizes doing both at the same time: “I check the route while looking at the map.”

Both 지도를 and 길을 use the object particle -을/를 to mark the direct objects of the verbs 보다 and 확인하다 respectively. Without them, the sentence would sound less clear or more informal: • 지도를 보면서 = looking at the map
• 길을 확인해요 = confirming/checking the route

확인해요 means “check,” “confirm,” or “make sure.”
찾아봐요 means “look (something) up,” “search for,” or “try to find.”
If you want to say “I look for a street,” you could use 길을 찾아봐요, but if you want “I check or confirm the route on the map,” 확인해요 is more precise.

Past tense:
• 지도 를 보면서 길을 확인했어요.
Future tense:
• 지도를 보면서 길을 확인할 거예요.

Yes, it’s grammatically correct.
• 길을 확인하면서 지도를 봐요 focuses on “I look at the map while checking the route.”
The nuance shifts so that “checking the route” is the first (concurrent) action, and “looking at the map” is presented as the main action. In practice, the original word order is more natural when you want to emphasize “using the map” as the tool for confirming the route.