A statement of purpose explains why you want to study a specific programme, what prepared you for it, and what you intend to do afterwards. Admissions committees read hundreds; the ones that work name the specific faculty, labs or modules that drew the applicant to that department, because generic enthusiasm is indistinguishable between candidates.
Usually 800 to 1,200 words, or one to two pages, unless the university states otherwise. Follow their limit exactly — exceeding it is a common and avoidable rejection reason.
An SOP is academic and forward-looking: your research interests and goals. A personal statement, especially in UK applications, allows more personal narrative and motivation.
For master's and PhD applications, yes. It is the clearest evidence that you chose the department rather than the ranking — but only name people whose work you have actually read.