Masterpiece gets involved in these productions at various points in the process, depending on the show. Sometimes, yes, we generate suggestions for which books are ripe for adaptation. Sometimes we get involved at the scripting/casting stage. And sometimes we do buy the shows after they're finished. Basically we're looking for, well, Masterpieces!
The air dates on PBS differ from those in England primarily because whichever channel in England is airing the program has its own schedule to manage, as does PBS. Masterpiece airs on Sunday night and we might want to make sure, for example, that we have five Sundays in a row, uninterrupted by holidays, to air something like Little Dorrit. There have been occasions when Masterpiece has aired a title in the U.S. before it aired in England.
Regarding the question about editing to time... Sometimes we might feel that the show would benefit by being slightly tighter. But more commonly, editing is due to odd lengths. The BBC has long had a very free-wheeling schedule. If you've travelled in England, you may have noted that programs might start at 5 minutes past the hour, 10 minutes past, etc. This flexibility allows the BBC to air shows of odd lengths. American television, by contrast, is really ruled by the clock! We need Masterpiece to begin promptly at 9:00. And whatever show is airing next needs Masterpiece to end promptly as well.
Because these films are works of art in their own right (yes, I do believe this), decisions have been made all along, about what to leave in and what to take out. The book's author made such decisions, the screenwriter made more, each performer makes decisions about how to say each line, the director makes still more choices, and so forth. Each iteration of the film is its own piece of art.
Reading some of the books has helped me on occasion to understand parts of the puzzle that may have gotten altered throughout this artistic process...
For the DVD's that you can purchase and whether you receive the full versions or not, please read Cinthia's answer in the comments.