Learn English – History of “System” in English language

Yes, grammar rules have changed considerably over the years. Original Chaucer is barely comprehensible to those used to just modern English; patches of Shakespeare and his contemporaries are a little stilted to modern eyes; even authors as recent as, say, Dickens or Austen write in a style that is somewhat different from the modern style. However, the more recent authors are much more readily comprehended than the more ancient authors.

However, there is also perhaps more continuity in the grammar rules than in spelling. That is, many key aspects of English grammar were also present in the Medieval period; a lot of the time, it was just the spellings and inflections on words that was different. There's some gross over-simplification in there.

I'm not sure that 'caste' is the correct term to use; 'class' certainly would be more normal. The main difference between the speech of 'peasants' versus 'clergy' or 'noble' would be in degree of literacy. Depending on the exact era, one factor might be that the 'noble' would speak French first, maybe Latin second, and English possibly a poor third - in the (first half of the) 12th Century, say. The clergy would probably speak all three contemporaneously, but would certainly know Latin since the liturgy was all Latin at the time. The 'peasants' might very well not really understand Latin properly, though they might well recognize passages from church; they'd speak English, but probably not French.

A couple of books I have that are fairly accessible (not too hard to read) and may be of interest:

• "Our Language", Simeon Potter, published by Pelican. I have what appears to be a 1950 1st Edition (cost one shilling and sixpence; it looks like I got it secondhand for 30 pence), but it is still available on Amazon in more recent (1976) editions.
• "The English Language", Robert Burchfield, published by Oxford. Also available via Amazon, but apparently out of print.

I've heard that the word "dog" does not have cognates in any other known language

After your previous question on walk and talk, let's go at it again. First, etymonline (as well as other sources) note that the etymology of dog is still quite foggy. Second, the Old English docga was picked up in other languages, as noted by etymonline, giving the French dogue and the Danish and German dogge (referring to a specific breed).

Third, and most importantly, wiktionary cites the Proto-Germanic dukkōn (“power, strength, muscle”) as the most plausible origin, from which the verb dock also comes. In other languages, the Danish dukke (“doll”) and the German Docke (“small column, bundle, doll, smart girl”) derive from this same root.

As a conclusion, I don't think you can find what you are looking for. There may be words with an etymology so unclear that they might not knowingly be related to any others in known languages, but I don't think you can ever formally exclude the possibility of related cognates.