Disclaimer: I tried to keep this simple but ended up writing a lot. You said you didn't want to hear about "every freaking Kingdom" but I'm not sure how to explain the history of Britain and its many many ethnicities, whilst also answering who are the Normans without doing that. So... sorry!

You have most of the building blocks but there are some errors and some things are in the wrong order. I'll try to give a basic run down.

Roman Britain happened in the first century AD. Before that were the native inhabitants and to be honest, not a great deal is known about them. They are known variously as Brittonic People, made up of many cultures including Celtic and Pictish (Scotland).

The Romans came and pushed the natives around but as you have intimated, the Romans didn't have the level of cultural impact that they did elsewhere in Europe which is to say that local languages survived. Eventually, the Romans withdrew leaving the Brittonic people to their own devices.

This is where the Anglo-Saxons come in but actually there are multiple different Germanic tribes invading the land. Angles are distinct from Saxons, and you also have the Jutes. These Germanic tribes are distinct from one another, coming from different parts of modern day Denmark and Northern Germany. They each successfully invaded the British island and pushed the Brittonic people, the Celts into the edges of the island. Basically they pushed them into what would be Wales and up into Scotland. Gradually, 4 distinct Kingdoms in what would become England emerge. You have West Saxons or Wessex in the South west, Kent in the South East, Mercia in the midlands and Northumbria in the north. We are talking about roughly 500 AD at this point so as you can see, we already have many ethnicities bouncing around in Britain.

Fast forward a couple of hundred years and now we have the famed viking raids. The Vikings are really just the Danish who invade and plunder without necessarily a national backing. They're kind of out for themselves. Known as vikings or Norse and they spread out and invade in all directions. They end up settling in the East of Britain, modern day Essex, and the North, re-establishing the old Roman city of Eboracum as Jorvik (now York). They take over swathes of the country leaving the 3 southern Anglo-Saxon Kingdoms in a dire state. Wessex under Alfred manage to push back the Danes. He takes over Kent, takes over Mercia through diplomatic marriage, strengthens defences throughout his land and essentially kicks out the Danish viking.

With this, Alfred and his successors become the first Kings of all England. The Celts are still squeezed out into Wales and Scotland and even Ireland.

Elsewhere the Danish/Vikings/Norse were settling in Dublin, the Orkney Isles north of Scotland, Iceland, and Northern France. The Northern France part is important because the vikings here establish Normandy. In fact the name Normandy is derived from Normanii which was a Frankish word for Norse Men, which literally means North Men. See, the vikings were harrying the Franks as well as the Brits. The Franks basically said, ok you can settle that northern piece of land if you leave us alone for a while. And so Normandy, a viking enclave in what would become Northern France was established.

Lets leave that aside and switch back to England and fast forward again to the early 11th century.

England is now well established as an entity, the Celts are still holed up in Wales/Scotland/Ireland. The Danes come invading again under Svein. They conquer and rule for a time, Cnut being quite a famous Danish King of England. The Anglo-Saxons (or English) hit back, there is a back and forth between the Danish and the English for a few decades. Eventually the English re-establish hegemony. There is some intermarriage etc even in the royal families.

1066 roles around and William, Duke or Normandy invades England successfully. Why? Well because of course by this point he is a cousin of a former English king since he is a direct descendent of the Danish vikings himself. He felt the throne of England was his by right and he went for it and won.

The Normans were the last to conquer Britain even to this day, all viking activity happened before this. But to answer your question directly about who were the Normans, well they were not very far removed from vikings themselves! They were Norse, settled in what today is northern France, they owed loose allegiance to the West Frankish (or French) kings but wasn't really very French.

To answer some of your other questions, yes it creates a lot of confusion using modern national names to describe old or ancient civilisations. In the time period we're talking about West Francia wasn't France yet, East Francia wasn't Germany yet. Normandy wasn't France, it wasn't even West Francia, and it wasn't Danish either, it was simply Normandy. This is why it is remembered as the Norman invasion, not the French invasion - because it wasn't French! At this point in time England was indeed England but it was only a couple of hundred years old as we have seen there were various Kingdoms before that.

I'm no expert on languages but hopefully this narrative has given you an insight into the multitude of ethnic groups moving in and around the British isles through force or otherwise and bringing their languages with them as they conquered. Many of these languages amalgamated over the years to become English which as you state (and the narrative here should make obvious) is a Germanic language, not a Romance language. But yes there has also been some centuries of borrowing from Romance languages, namely old French which have also influenced the language. The Normans did bring old French with them and it was the state language right up until Edward III changed it to English in the 14th century. But the locals spoke English all through that time, it was only the Norman aristocracy that were speaking French languages.