It depends course to course, school to school. For example Bath is a notoriously mathsy architecture course and you'll have more emphasis on the engineering side of things in the form of lectures, which will translate into your studio projects. This means you'll be learning how to do calculations related to structures or to do with lighting and heating (which will start off easy and become more complex year by year). Conversely, you'll likely have less in the way of essays at schools that have a focus on the mathsy side or are all about the creative/conceptual side, whereas some of the more 'academic' architecture schools like Cambridge and Edinburgh will set you more essays. These will be based on whatever you learn in the history and theory lectures, and may ask you to compare and contrast buildings, discuss the influences of certain architectural styles, etc. You may also get extended-essay-style pieces of coursework that might involve (basic) calculations and analysis of structural aspects of a building (I know that Edinburgh does this in first year, for example).
All that being said, the vast majority of architecture courses are almost exclusively coursework-based, meaning most if not all of the focus is on the design work (drawings, models, CAD, etc.) you produce in studio. Even for the more mathsy or academic courses, the majority of your marks come from your studio work (the minimum being Cambridge with 60% studio coursework, 40% written coursework and exams).
As for the hardest parts, I can't speak from experience as I haven't started the course yet (in Year 13 currently). But from what I gather it seems like the 'hardest' part is completing the design projects you get set in studio, not so much in terms of difficulty, but just the sheer amount of time and effort it takes to get everything done in time.
Have you started thinking about which unis you'd like to apply to and/or what sort of architecture course appeals to you?