I assume William would have spoken Norman, yet as he entered what's now London to be crowned how would he actually have spoken with anybody? Surely all subjects as well as the Anglo-Saxon nobility would speak Anglo-Saxon. Was Latin used as a bridge between Norman and Anglo-Saxon? Even when William replaced many of the Anglo-Saxon aristocracy with Normans how would he have informed the Anglo-Saxon ruler that he was being replaced/having his title revoked? Even if William didn't come into contact with many Anglo-Saxon subjects at court how would his nobles talk to their new vassals? Was their a system where there would be subjects who spoke both Norman and Anglo-Saxon and would effectively 'translate' the wishes of the Norman aristocracy to their new subjects? To what extent did the Anglo-Saxons understand the events occurring in the new nobility?
I'm going to try and answer your questions one by one!
William and his court, that he brought over from France, spoke exclusively French. So much so, that French became the language that the nobility spoke and wrote in, as well as the rise in the use of French names for children born after 1066.
Latin was used for governmental records as well as church records; it was the language that mostly everyone could speak or read (depending on their level of education).
However! William used English in a smattering of his decrees and letters and various other communications. This was to make himself seem more relatable to the common Englishman; add in an element of trust. He could understand English, but not very well. Most communication was done via Latin and letters, as well as simply various translators going about the place while William was in Normandy.
The Saxons were somewhat furious about this whole debacle. You might have heard of the Harrying of the North, where William, in response to a handful of quickly-suppressed rebellions in 1070, took the entire North of England with an army and torches, and burnt the land; rendering it useless for crops and ensuring a dependence on the Crown. The Saxons did try to rebel, but William was aptly named Conqueror and quickly shut them down; cementing a Norman rule fairly quickly until the Danes started to invade.
Sources: The Struggle for Mastery - David Carpenter
England and its Rulers, 1066-1272 - Michael Clanchy
Uniting the Kingdom?: The Making of British History - Alexander Grant & Keith Stringer