If so and you can't find the information you want on their site you can submit your questions to them on the online form linked to on the webpage I've given here. Additionally someone on this site will probably answer your query re whether or how being on one of their courses might affect your ESA. Regarding your question
"Do city lit informs esa about your bookings please?" I think it would be better if you simply asked City Lit directly as surely they would know the answer better than anyone here, how can we know what this organisation might do?