1. A:Where is the shoe store?
B:It's on/at the corner.
Q: at or on? Which one? What's the difference?
2. A:How can I get to the bookstroe?
B:Turn left on the next corner.
Q: Sometimes we don't need the before next. Do we have to add the
And more Ex: We went to school next day.
We went to school the next day.
3. Please turn left on/at the corner of Park Rd. and Patty St.
Q: on or? at which one is right?
And more Ex: Turn left at/on the corner.
The mailboxis at/on the corner of the street.
I can't really comment on the grammar, but I can say what a UK native speaker would use.
If the corner is where something is, we use "on". If it's where we do something we use "at".
"Go right at the next corner. You'll find the news stand on the next corner on the left."
And, yes, we'd always use "the".
"How do I get to the station?"
"Turn left at the second corner on the left and the entrance is on the corner of High Street and Park Lane."
Similarly, we'd generally use, "the next day."
buggles (not a teacher)