Hello, Elle!
I put Lurpak salted butter on my toast.
If you look in Chambers you will see that a meaning of "face" is "the front or surface of anything.
So coat just about means that.
As in a coat of paint, possibly.
"See" is under "V" in Anne Bradford's Dictionary, too.
There is another abbreviation in 20d, "PPE" for "course".
I came across this before.
It is a University Course of "Philosophy, Politics and Economics".
Non-uni folk like me would struggle with it.
Make good use of your Dictionaries, they will help you.