This is a charity that meets the legal definition of a charity and then registers with the charity commission for their nation (there are separate charity commissions for England and Wales, Scotland and Northern Ireland). Not all charities are registered and very small ones are not eligible to register.
A particular way of studying something. Examples of research methods include interviews, surveys, focus groups, analysis of documents and so on. Research methods can be quantitative (involving numbers through surveys) or qualitative (finding out about people’s experiences and how they make sense of the world).