13 Beamer columns are basically just minipages with some `\hfill` between them to distribute them across the page (and a couple of extra features like making them overlay aware etc.). So I would not say "don't use minipages with beamer" but rather that is normally easier to use columns instead of minipages.
13 The syntax of `\let` is `\let<token 1><token 2>` where `<token 1>` should be a control sequence or active character. It assigns to `<token 1>` the same meaning `<token 2>` currently has (there are some specialties regarding equals signs and space tokens, something we don't have to care for here).
8 An arc between two points on a circle is not uniquely defined, there are two options. In the case at hand, there is also a midpoint close to `C` of an arc between `A` and `B` on a circle with center `O`. This is why the following code has two angles, `\n1` and `\n2`, which differ by `180`. While in this example the angles of the points are known, in general they may not be, which is why they get determined with the `calc` library. In more detail, after saying inside the `let ... in` block
8 `csquotes` is one of the packages which need to be loaded before `\AtBeginDocument`. Instead you could use the `etoolbox` package and load it at the end of the preamble (csquotes would anyway load etoolbox, so no real disadvantage from loading it):