-Tell me where I am flawed or correct in my basic understanding of the Celtic people/Celts:

The Celts are more of a language and culture, rather than a specific people. The Celts originally came from central Europe (modern day Austria-ish?). During the rise of Rome and the expansion of the Saxons, etc. the Celts were pushed out and they migrated to England. This is where the ancient Britons/Celts, Picts, etc. originated (or were there inhabitants in England before the Celts?). When the Romans invaded England they were met by the Celts (who had migrated from/were pushed out of Europe). After the fall of Rome, the Saxons, Normans, and others pushed into England. From here, the Celts were either defeated in battle or they integrated with the more powerful invading forces. Some even escaped to modern day France where the celtic language is still spoken. While people of England today are descendants of invading Germanic and Viking tribes, their genetics are more rooted in the ancient Britons/Celts that had migrated and were pushed out from Europe.