I read ages ago that they would go only as far as ca. 2002, because they don't want to get involved with too modern days and because it's easier to work with hindsight and historic events that are more or less concluded (saying less because things about e.g. Diana are still coming out (Panormana/Bashir, anyone?) and other things will still come out about the past, as is usual, really).
Each series was supposed to be one decade, I was a bit surprised by the announcement of a 6th series, but I suppose covering ca. 1990 - 2002 will take quite a lot.
I think the idea that Olivia's Liz is "harder" due to age and experience than Claire's is a good theory, considering Liz apparently was never that warm to begin with and had more experience by the 1970s and 1980s. I think part of the dislike of series 3 portrayal of the queen is the shock in change.
Apparently the Wessexes were big fans when series one came out and watched it with Liz Saturday evenings at Windsor during their regular informal dinner. Not sure much beyond that has come out.