In Expressions^x, Direct questions^x, Conversations^x

I know 'would' carries many meanings. My problem is sometimes I find it difficult to tell which meaning the speaker uses. I think I understand its hypothetical usage, and in some contexts, its politeness usage. Below is a post that has several woulds I have trouble interpreting. I also...

Dear teachers, Would you please correct my answers? But before that I’d like to ask you if I understood the meaning of the underlined expressions or ideas. Furthermore, I’d like to ask British teachers if they confirm what she says about the “British thing” and give me more elements about...