1. You can hope we correct it, or you would like us to correct it. You cannot hope you would like to. You don't talk like that in Korean, either. I don't know a word of Korean, but I'm still willing to bet you don't talk like that.
2. If you're doing a puzzle, why are there errors in your writing? What does puzzle have to do with writing?
Anyway, if you're asking fro something:
I wonder if you could correct my errors.
I wonder if you could help me to correct the errors.
Could you please....?
Would you please...?
There are other ways, but I think four is enough for now.