I had never heard of a breakfast booth, but I just googled it and discovered that this is an accepted term. It appears that 'breakfast booth' or 'breakfast nook' is a three-sided arrangement of padded benches around a table, designed as a cosy eating space within a larger room. Well, I have learnt something there! I have never used this term, but I might start using it now. Thank you for this.
And, yes, 'English composition' makes sense. A composition is a piece of creative writing or a student's essay on a particular topic. If you write this in English, this is an English composition.