When I want to know what form a word has say in 12th century (end Old English, begin Middle English), 14th century (end Middle English), or any other time in England history, I only need to track the word's etymology, and I've got the evolution of said word. But what about the grammar? Should I assume similar rules as the current ones? Is there also any consideration depending of the caste of the person speaking, such as a peasant in comparison to a clergyman or a noble? Is there any interesting reading or online resources on the subject I should know about? (If the scope of the question is too broad, area of interest are 12th century and 14th century.)
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:
I concur with the previous answer, though I would point out that part of the difficulty with Chaucer and Shakespeare is that the author was writing in verse rather than prose. Grammar and word order are often modified to fit the content (meaning) to the form (meter, rhyme, etc.) when an author is writing in verse--this is still true today.