A PhD SOP is a research proposal in disguise. Committees are assessing whether your question is viable and whether a supervisor in that department can supervise it — so name the question, the methods, and the specific faculty whose work yours extends.
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.