(Part 2) I think "bleak" is a misprint for "beak." (Yes, John thinks so, too). "Beak" is British slang for "a judge," especially a low-ranking local judge. Again, this is the language Bertie Wooster would have used.
"Cheek" means boldness, like an impertinent teenager who "talks back." For example, suppose a parent says "Please eat your vegetables, they're good for you, there are starving children in Zambia who would love those vegetables," and an eleven-year-old boy retorts "And I would love to send my vegetables to them." That's "cheek."
In more straightforward English, "Bertie Wooster, the foolish aristocrat P. G. Wodehouse wrote about, seems to be forever pulling practical jokes, like stealing policemen's helmets off their heads, and then having judges let him off with almost no punishment, for being obnoxious."