Learn Hardcore Korean: sageori motungie pyeonuijeomi boyeo? - Do you see a convenience store on the corner of the intersection?

보여? comes from the verb 보이다 (‘to be visible’), not 보다 (‘to see something’).
In casual speech, 보이다 → 보여 (Present tense informal).
With a rising tone (보여?) it asks “Can you see [it]?” or “Do you see [it]?”, focusing on whether something appears in your view rather than the action of seeing.

Why is the convenience store marked 편의점이 and not 편의점을?

Because 보이다 is an intransitive (stative) verb meaning ‘to be visible.’ The thing that is visible is the subject, so it takes -이/가.
If you used transitive 보다 (‘to look at, to see something’), you would say 편의점을 본다 with -을/를.
In very casual speech you might even drop -이, saying 편의점 보여?, but grammatically the subject marker is -이/가.

Why is there no 의 between 사거리 and 모퉁이?

In Korean, when one noun directly modifies another as an attributive, you often omit 의.
사거리 모퉁이 naturally means “corner of the intersection.”
사거리의 모퉁이 is grammatically possible (more formal/literary) but sounds stiff in everyday conversation.

Why does 사거리 모퉁이에 use -에? Could it be -에서?

-에 marks a static location—where something exists or appears. Since 보이다 describes where the store is visible, we use -에.
-에서 marks where an action occurs. E.g. 모퉁이에서 기다려 (“I’ll wait at the corner”) involves the action of waiting, so it needs -에서.

What level of politeness is 사거리 모퉁이에 편의점이 보여?, and how can I make it more polite?

As written, it’s 반말 (informal/light casual) suitable among close friends or younger people.
To soften or be polite, you can say:
• 사거리 모퉁이에 편의점이 보여요? (everyday polite)
• 사거리 모퉁이에 편의점이 보이나요? (more formal/polite)
• Or even 사거리 모퉁이 쪽에 편의점이 보이시나요? (very polite/honorific)

Could I say 사거리 모퉁이에 편의점 있어? instead of 보여? What’s the nuance?

있어? asks simply “Is there [a convenience store]?” (existence).
보여? asks “Can you see it?” (visual confirmation).
If you want someone to check presence in general, use 있어?; if you want them to look and confirm visibility (maybe it’s hidden or small), use 보여?.

What’s the difference between 모퉁이 and 모서리?

모퉁이 refers to the corner of a street, building, or general place (e.g. “street corner”).
모서리 refers to the edge or corner of a solid object (e.g. corner of a table, paper).
For 사거리 모퉁이 (“intersection corner”), always use 모퉁이.

What’s the difference between casual endings 보여?, 보이니?, and 보이냐? when asking the same question?

• 보여?
– Standard informal (friendly), neutral tone among peers.
• 보이니?
– Also casual, often used by an older speaker to a younger or for a confirmatory tone.
• 보이냐?
– Rougher/more forceful casual, sometimes masculine or used in storytelling; can feel harsh if misused.