I will start this response by immediately telling you that unfortunately and quite possibly one of my main reasons for loving early medieval Scotland history is that there aren't very many sources still around about that time period, this including the Briton's of Strathclyde. Early Medieval Scotland likely did have some monastic chronicles from this time period as we see glimpses of these appearing in later sources but these originals no longer exist.

From what we know the Briton's of Strathclyde - also known as Alt Clut - were a celtic people who held sway in South-west Scotland and parts of North West England - particularly in Cumbria which is why they are sometimes refered to as Cumbrian - and existed on and off as an independent entity from around the time of the Anglo-Saxon invasions in the 5th century until their eventual assimilation with the Scottish Kingdom sometime in the 11th century - possibly the 12th century I really can't stress enough how little information we have about Scotland at this time. They are the remnants of the celtic peoples who had inhabited that part of Britain since before the Roman Invasions and likely spoke a language in the same branch of Celtic Languages as Welsh and Breton known as Cumbric.

Therefore they differ from the many people around them such as the Picts to their North East - natives to Britain but distinct enough that we wouldn't class them as Britons -, the Scots to their North-West in Argyll - Gaelic settlers from Northern Ireland -, and the Anglo-Saxon people of Lothian to their South-East and East - who had invaded and displaced the pre-existing Britons of the lands that they settled and can almost be seen as a last bastion of Brythonic culture in the North of Briton.

There are also traces of Gaelic peoples in the very very South-Western parts of Scotland but even less is known about them and their existence is debated heavily possibly being pre-viking but most likely being the colonisation by Norse-Gaels after the Vikings.

So once we get to the beginning of the Viking age in the late 8th early 9th century we see an fairly autonomous people located in the South-West and North-West of Scotland and England. To address your questions directly, No the Britons were not related to the Vikings. However, South-West Scotland did see extensive interaction with Norse and Danish peoples and a little bit of colonisation.

Were they remnants of Rome? No the Britons were the native Celtic people of Britain and are descended from the Celtic people that had come under the control of Rome after their invasion and were liberated after Romes withdrawal from Britain.

Did the Briton of Strathclyde found wales? No while the peoples of Wales were also Britons they were also distinct, speaking a different albeit similar language. Wales was also a very fragmented country split between a number of different British warlords and tribes along with a number of Anglo-Saxon incursions.

Throughout the time between the Viking age and the 12th century Strathclyde would be dominated by its neighbours, throughout the 9th century the Picts would dominate Strathclyde and while Strathclyde would see much more independence at times the Pictish and later Scottish kingdoms would dominate it.

After the reign and defeat Fergus of Galloway in 1161 the limited evidence we have appears to show us that the Kingdom is absorbed by the growing Kingdom of Alba and the Britons of Strathclyde disappears. To such an extent that by the 12th century the language of the Britons becomes extinct - although this is likely a process that had started many decades before with Scottish influence and culture appearing to dominate the British nobility and culture of the region.

Strathclyde did however retain some distinct characteristics as it has been argued that the title of "Lord of Galloway" possibly acted in a similar manner to the English "Prince of Wales".

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On to books, I will be listing my sources for this information as part of standard /r/AskHistorians rules anyway and I recommend all of those texts but will highlight a few and talk about the problems with others.

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I highly recommend the first three books in the current edition of the New Edinburgh History of Scotland Series:

"From Caledonia to Pictland, Scotland to 795" by James E. Fraser

"From Pictland to Alba, 789 - 1070" by Alex Woolf

"Dominion and Lordship Scotland 1070 - 1230" by Richard Oram

These are an excellent series of books for giving a good grounding on Early Medieval Scottish History. They are more general readings but these Historians have all done fantastic work in their field. I would personally recommend Woolf who's pioneering research about 10 years ago flipped perceptions about Pictland and in particular the power base of the Kingdom being in the North of Scotland and not in the Firth of Tay.

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"Early Sources of Scottish History - Volume 1 and 2" by Alan O. Anderson

Anderson's work is extensive and is a blessing. His two volumes are English translations of most of the early sources that deal with Scotland in the Early medieval setting. However, the biggest thing to recognise with Anderson's work is that these books were published in 1922. This means that many of Anderson's comments and observations are no longer recognised by Historian's as correct - a good example is the assumption that the Pictish Kingdom of Fortriu being based in the Tay, partly based on racist assumptions about the Highlands of Scotland - which as we know from Woolf's work in recent years is no longer completely accepted. Furthermore there are much more modern translations of some of these sources around - these transaltions unfortunately often locked into academic papers that you have to pay for to access. However, Anderson's volumes are broad and have almost all the sources translated into English.

Furthermore Anderson's texts are online for FREE

Volume 1: https://archive.org/details/cu31924028144313

Volume 2: https://archive.org/details/earlysourcesofsc02ande

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Full List of Sources:

"Dominion and Lordship Scotland 1070 - 1230" by Richard Oram

"Early Sources of Scottish History - Volume 1 and 2" by Alan O. Anderson

"From Caledonia to Pictland, Scotland to 795" by James E. Fraser

"From Pictland to Alba, 789 - 1070" by Alex Woolf

"The Makers of Scotland" by Tim Clarkson

"The Last of the Free" By James Hunter

EDIT: Changed some Grammer, corrected dates and added Links to Anderson's work.