I'm not sure I can answer all your questions, but I will try.
The idea of the Domesday book is thought to have sprung from a discussion between William the Conqueror and his witan (wise men/advisors) in 1085. The actual survey was carried out in 1086 and most likely ended with William's death in September 1087. (There is still scholarly debate about when the survey actually concluded. The most common explanation in the sources I have encountered is that the death of a King is usually followed by a "lawless interregnum" period. This theory is supported by the incomplete Domesday volumes.)
The survey itself was conducted by seven or eight groups of commissioners, legati, or barons. Moreover, the shires of England were divided into seven circuits to allow for one group of commissioners to examine and record a large number of counties. For example, the first circuit to appear in the Domesday book was comprised of Kent, Surrey, Sussex, Hampshire, and Berkshire. (There is more scholarly contention on the number of circuits. Namely, some historian argue that there may have been an eighth circuit comprised of solely Yorkshire and Lincolnshire)
Once in a county, the commissioners were required to obtain the name of the estate, who held the estate in the time of King Edward, who held it in 1086, how many hides there were, how many ploughs there were, how many slaves, freedmen, and so on. Furthermore, this information was to be recorded three times and additional mention was made if there were more assets. The information gathered from the inquiry was then regrouped under the names of the King and his tenants in Chief.
I'm not sure if I have a concrete answer concerning the accuracy of the Domesday book. The sources I've read make reference to later commissioners utilizing the information of the Domesday book, but I cannot find a clear example.
Sources: Galbraith, V. H. Domesday Book: Its Place in Administrative History. England: Clarendon Press, 1974.
Roffe, David. Domesday: The Inquest and the Book. Oxford: Oxford University Press, 2000.