The last part is easier to explain. 위를 보면서 걸어요. I'm sure you know 걸어요 means "walking", 위 here means above or up, 보다 is to see of course.
~면서 added to verbs means "while" so that means the two verbs in the clause will be connected in time. 영화를 보면서 저녁을 먹어요. I eat dinner while watching a movie. 너가 부엌에서 찾으면서 내가 욕실에서 찾을게. While you look in the kitchen, I'll look in the bathroom.
Adding ~게 is a bit stranger. It's important to distinguish between ~게 and 하는 게. 하는 게 is just another way of saying 하는 것. ~게 하다 is commonly translated as "so that x happens" or maybe "so as to (not)." It's hard to make simple sentences that are realistic...잘 들을 수 있게 분명히 말해주세요 = Speak clearly so I can hear you well.
장을 보는 걸 잊지 않게 퇴근할 때 나를 전화해줘 = When I leave work, call me so I don't forget to get groceries.
More about ~게 can be found here: https://www.howtostudykorean.com/unit-3-intermediate-korean-grammar/unit-3-lessons-51-58/lesson-56/
Let me introduce this grammatical principle to you with one simple example. To create this meaning of “to make” or “to let,” you can attach ~게 하다 to the stem of a word. The subject of the sentence “makes/lets” the object do that action. For example:
나는 그를 공부하게 했다
Two common English translations for this Korean sentence would be:
I made him study I let him study
I’d like to discuss why the translations of “to make” and/or “to let” are used in this situation. In English, the word “to make” is more related to forcing a person to do an action; whereas “to let” is more related to allowing a person to do an action. In both cases, the subject is doing something (either forcing or allowing) that, in the end, influences/causes the person to do the action.
The Korean usage does not distinguish between “forcing” or “allowing.” It simply indicates that the subject does something (regardless of it was by “forcing” or “allowing”) that causes/influences the rest of the clause to occur. Therefore, a more accurate translation might be:
나는 그를 공부하게 했다 = I did something that caused/influenced him to study
Therefore, it’s not that “~게 하다” can have two translations – but rather that the meanings of “make” and “let” are very specific – and both of these meanings can be encompassed in the idea that “one causes/influences the action to occur.”
"I look up while i walk, so the tears don't flow" shouldn't this also be correct?