I can't give you any definitive answers, but as this question has been open so long I guess some plausible speculation is acceptable. I imagine that the move from SVO to SOV worked like this.
The earliest stage that is of interest to us is when word order was very free due to ample inflections, but with a preference for SOV as the default. People deviated from SOV when they wanted to stress something.
As it was so easy to stress something in this way, people overdid it, as they always do. They started stressing a part of speech that didn't really need stressing - the subject - in every other sentence, then in almost all sentences. The few SOV sentences, which didn't stress anything, tended to move into the background.
Something similar can be observed in the unusual syntax often used for German jokes. As is well known, in Germany it's illegal to confuse the public by telling a joke without wearing suitable attire or following the correct word order. Where many English jokes start with "A man walks into a bar", German has this:
- Kommt ein Mann in eine Kneipe (literally: Comes a man into a pub)
Note the meaningless stress on the verb in this example and the next one. It's not just the first sentence, either. Often most sentences have this structure, such as:
- Sagt der Mann zu der Frau (literally: Says the man to the woman)
In the context of a German joke using this attention-grabbing word order, sentences without it tend to stay in the background.
That you could now put a sentence in the background by following the old-fashioned word order must have made it possible to use such sentences as a substitute for subordinate clauses. Of course for us SVO is just normal, so let's model this by using VSO instead.
Meet an American rancher and a German farmer. They are arguing who has more land. Says the American, "I have so much land that I need an entire day to drive around it." Replies the German, "Years ago I also had such a slow car."
The second sentence is in the background as if it was a non-restrictive relative clause attached to the first. ("Meet an American rancher and a German farmer, who are arguing who has more land.") For this interpretation it plays a role that the object - to which the relative clause refers - comes last as in our artificial VSO example, or historically (if I am right) in SVO. The interpretation would make less sense if the first sentence were in SOV order.
So the word order change from SOV to SVO had two effects: (1) One could distinguish main clauses and subordinate clauses even before unambiguously coordinating words such as relative pronouns existed. (2) Subordinate clauses referring to the object of the main clause could be placed immediately after the object. (Few subordinate clauses refer to the verb.)
So this is my response to Question 1: It may well have happened the other way round, and by the mechanism I described.
Question 2: The other modern Germanic languages are more or less spoken today where they originated and with only average contact to other languages. English is the result of transplanting and mixing dialects spoken in northern Germany and southern Denmark to a country with a lot of Celtic speakers and later on adding a French-speaking ruling class. Apparently this (or something else) has made it progress faster on the path from SOV to SVO, on which V2 is just an intermediate stage. (German word order is clearly in motion. Recently it's becoming more and more acceptable to use V2 instead of SOV in clauses introduced by weil, for example. Also in some cases, Dutch and some German dialects order non-finite verbs differently than Standard German does: German "dass sie bezahlt werden sollen" vs. Dutch "dat ze betaald zullen worden" or "dat ze zullen worden betaald" vs. Flemish "dat ze zullen betaald worden".)
Question 3: Apparently, after a previous consensus that Old English was V2, there is currently a new discussion on this. It's not hard to find interesting recent work. Your proposal of its being left-peripheral, if I understand you correctly, doesn't explain the 5% or so of verb-last sentences in it any more than V2 does.