Yes, I should have said that I assumed the question to be "What happened after the death of Edward the Confessor?"
You need to take care to write grammatically.
The answer makes the erroneous claim that Edward promised the Crown to Harold. On the evidence, Edward's intentions as to succession are unclear.
The invasion by Hardrada is an important fact. Harold spent most of the summer of 1066 with his army on the south coast prepared to face William, whom Harold knew was intent on invading. Weather or supply problems kept William in Normandy. Harold then had to react to the invasion in the North. William landed unopposed while Harold was fighting in Yorkshire.
William was intent on regime change. He had a relatively small force and there was no large scale population movement after the conquest. Eleventh century monarchies were personal and not based on ethno-nationalism.
After defeating Harold William replaced the Saxon aristocracy with his Norman followers. His later military campaigns in the north of England reduced the population there.
William was interested in property, to bolster his rule in Normandy. Hence he commissioned Domesday Book, a survey and record of all land holdings in England.
The peasants continued their daily lives with rulers speaking Norman French instead of Old English, and with changes in the law. Modern English is a Germanic language heavily influenced by French, because of the conquest.
William could not transport castles across the channel. Eleventh century ships were under 100 metres in length. You can see the ships on the Bayeux Tapestry. The Normans initially built wooden and earthwork castles, later replacing these with stone castles using local labour.