I am only allowed to answer the first question. Any other questions must be posted separately.
In the poem "We Real Cool" by Gwendolyn Brooks, there are two notes after the title, before the poem begins that state:
The Pool Players
Seven at The Golden Shovel
I believe these lines are singularly important to answering your first question. The "Pool Players" are the "we" in the poem. They seem to be playing pool when they should be in school. "Seven at The Golden Shovel" most likely indicates that there are seven youngsters, cutting school, playing pool ("strike straight") at the pool hall called "The Golden Shovel."
These are no choir boys: they "sing sin," and "thin gin." They stay out late. And the author presents a perception that in doing these things, the young group of "rebels" believe they are "real cool," though we don't get the sense one way or the other, as to whether the author agrees with their viewpoint.