So, we all know the Arthurian legend. What kind of weapons did the Britons use to fight the Saxon shield walls? Was there a dominant kingdom or was there really a High King like in Ireland? How... was the ruling done? What was the average size of the armies? Feel free to add any information you want.
If you're able to get your hands on it T.M. Charles-Edwards magisterial tome will answer as many of your questions as can possibly be done. Wales and the Britons: 350-1064, Cardiff, 2013. Unfortunately our sources are rather paltry but his work, if rather oriented on Wales, represents the pinnacle of modern scholarship.
Unfortunately, for many of the questions you are asking, the best answer is generally "we don't really know". The term Dark Ages is widely criticized for misrepresenting the post-Roman world, and quite rightly so, but if it applies anywhere, then it definitely applies to the century or two following the end of Roman rule in Britain. We have essentially two written sources for this period: the histories of Gildas and of Bede, and the latter is based in part upon the former. And from what I recall, neither is much concerned with details like weapons, governmental practices, or army size.
According to Bede's account ( Ecclesiastical History, Book I, Chapters 12-17; 20, 22), the Britons in the aftermath of Roman occupation were largely unwarlike and unable to deal with the existing Celts and Picts, much less the Saxons and Angles who are later invited over as mercenaries. We get some of the names of leaders of the invaders, but nothing about how they ruled or how many men they brought. One exception to this rule, a leader named Ambrosius Aurelianus, has his own chapter, but even here, the most detail that Bede gives is:
"Under his leadership the Britons regained their strength, challenged their victors to battle, and, with God's help, won the day. From that time on, first the Britons won and then the enemy were victorious until the year of the siege of Mount Badon, when the Britons slaughtered no small number of their foes about forty-four years after their arrival in Britain."
So that's the level of descriptive detail that written sources for post-Roman Britain can provide. Archaeology can tell us a lot, but again, I don't know if it can really answer the questions you are asking for this time period.
There's more information available for Anglo-Saxon England before and during the Viking invasions--I'd recommend The Anglo-Saxons, by James Campbell, Eric John, and Patrick Wormald. (London: Penguin, 1991) It's a solid introduction and overview, with lots of images of archaeological finds, maps, locations, and other illustrations. My undergrad course on the Age of Bede used this as a companion to fill out primary sources and help place them in their context.
For more detailed military history of this period--attempting to answer the weapons and tactics part of your question--at a less-academic/more accessible level, you might enjoy some of Osprey's relevant books:
Late Roman Infantryman, AD 236-565
They're probably available on Amazon, and (WorldCat)[https://www.worldcat.org/] can tell you whether nearby libraries have them.