re: White Americans think they are mostly German but they are mostly British

If you come from Europe, you are made-up of three ancestries:

1) Hunter-gatherers who ruled Europe from 40,000 years ago up until about 8,000 years ago.

2) Neolithic farmers who came in from Anatolia starting about 8,000 years ago, making it to places like Britain by 6,000 years ago. They basically pushed the old hunter-gatherers to the Pacific coastal areas.

3) Then in Bronze age (3,000 BC) the Ukrainians came in and killed off most people in Northern Europe. They killed all the men and "married" the native women. (We know this through DNA sampling of ancient skeletons). They started the Corded Ware Culture which dominated Northern/Eastern Europe. They also invaded southern Europe to some degree, but didn't fully replace the populations there. These people would have brought in the original Indo-European language. This language would evolve into Germanic, Italic/Latin/Romance, Celtic, Greek, Iranian, and Indic/Sanskrit, among others.

Any movements since that time were simply these three groups spreading around within Europe. Romans, Celts, Vikings, Anglos, etc. All the same people with different admixture levels of the same three populations. For example, Greeks/Romans were heavier in Neolithic ancestry while Vikings/Anglos were heavier in Ukrainian bronze age ancestry.