1: Russel introduces the notion of sense data as things which are immediately known in sensation such as colors, sounds, smells etc. He does so because he states that nothing we se/hear/feel is definite, as it all varies by angles of viewing point, lights, which part of the body is used to feel etc.
The reason of this introduction is to separate sensations of truth from the truth itself, as the sensation is dependent on the sense data, which in turn is dependent on the relations between us and the object in question.
2: Both "proposition" and "statement of fact" are meant to refer to a level of truth in a statement. The difference between the two are that proposition is ones own acquaintance with a subject of matter, while the second is a more ”well established” conception of something. The latter has a higher sense of truth to it, as it is a view
3: The notion "definite description" means that when talking about description, definite description eliminates the possibilities of one referring to several objects. When talking about ”a man”, one may refer to any possible man, while when instead saying ”the man in the yellow hat with purple stripes” refers to a very specific man in singular form.
4: As far as I understand, Russel's argues that we can't know the nature of something without knowing all of it's "truth's" as well as it's relations to other things. He brings up the example of tooth ache, how we may be as acquainted as possible with it, giving some knowledge of it, but not the same amount which a dentist may have, which doesn't have any acquaintance with said ache at all. This leads to the suggestion that we cannot prove that the universe forms a whole "nature" so to say (or a "single harmonious system" as is written in the book), as we cannot say if anything has anything has unknown relations as, well... we don't know about them.
I do, to certain extent, agree with what you argue with regards to the idea that we cannot prove that the universe forms a "whole nature" but would argue that only because we are unable to know this it does not mean it isn't true since with time and study we have, through study of the universe, found evidence of connections which suggest a "harmonious system" like when we "found" the gold ratio or the fibonacci sequence.
SvaraRadera