A question to those knowelegable on english history.

When the normans invaded england how many where they? After the invasion did they make up a big chunk of the new english population?
Also the same question on the viking invasions. Did the vikings ever settle in england and if they did. Where there many of them?

The UK and scandinavia must have alot of comon ancestors. Todays english royal family, are they direct descendants of William the conquerer?

Would be ironic if the english royal family are descendants of the vikings while swedens current royal family is french.