It is probable that after this, some cataclysm came about and returned the culture level to stone age. Dwarves and halflings probably were assimilated into race of Men or died out, leaving little evidence of the existence of the old civilizations.
But you're forgetting that I have first bronze and first farming.
That is true according to our observations. However, playing the role of Silmarillionistic preacher, this doesn't mean that there couldn't have been unknown civilizations before the known stone age.
Ice ages and geological changes tend to be good at destroying evidence...
Even if it had existed, there would have been signs. Entire periods of existence do not simply disappear. (yes, I have read the rest of your post. I'm being specific here.)
That's true, of course. Unless Eru Ilúvatar or more likely some of the Maiar decided to remove the evidence...
At least they are plenty contradictory to the existence of the Divine Master Plan. God seems to be plenty good at cocking his plans up. First with the Eden debacle with the snake, then letting the world get into state where a purge was needed to restore some kind of plan, then it still didn't work out so he had to have a son and send him to wipe the humanity's collective ass clean, so to speak.
That is where the (?)issue of free will comes into play. God gave man free will so they could choose to serve Him. Some did not (hell, most do not now.). It's not that He let it get to that state, we (man) let it get to that state, and so God *ahem* cleansed it.
So is it acceptable for a teacher or a parent to let their children or students get into a mess where they have to be killed or at least given a severe beating to purge them of their stupidity?
Intervention at earlier time might have yielded positive results. But, accorting to the bible, God consciously allowed the situation to deteriorate to the point where it was apparently necessary to open the floodgates. Apparently, an almighty being considered it necessary to kill most of the land animals on Earth... So the question is, why allow free will if you're going to kill offenders anyway? Actually, sounds kinda like the argument that Islam is a religion of peace because it freely allows you to either convert, become a slave, or die.
...leaving little evidence of the existence of the old civilizations.
Or no evidence at all. There is none, zero, ziltch.
Similarly to earlier in your post, absence of evidence can also mean absence of evidence.
Do you mean that absence of evidence can mean evidence of absence?
No, it can't. Not really. Absence of evidence is good grounds not to believe in something, but it is never evidence of absence. It's always possible that dragons exist. Or existed. Or that God exists. It is improbable because there's no hard evidence supporting it, only N'th hand claims of information received from above, and no assurances whatsoever that any of this information in any form is really from the source it claims to be from.
Like I said, it's easy for me to write a piece that says it's a message from God. It would have been equally easy in the past when holy books were written. They might have been written under the influence, but I deeply suspect that influence was something else than God, possibly something more chemically based.
The writers might have even believed they wrote the word of God. That doesn't mean that they really were receiving signals from above any more than the "automatic writers" are receiving signals from extra-terrestrials (which I believe is an analogous phenomenon to the Prophets of the olden days).
The point is, if someone really believes that something, anything, is true, it's really hard for them to view the matter objectively.
But, by your criteria, anyone who can view the matter objectively will already not believe, therefore is also biased in favor of their own beliefs.
No, it means that anyone who can view the matter objectively will not believe in it for the sake of belief only. Objective view takes into account more than just what the source claims. Of course the Bible says it's from God, otherwise it wouldn't be a "Holy Book". But it never went through any kind of peer review program, so to speak. The regulators were all members of the church, the biggest edits having been done by the Councils of Nicaea that affirmed the canonical books of the Bible and left unsuitable materials out.
what makes a prophet different from false prophet?
These days? That there are no more prophets. Christianity and Islam agree on that one. 
I'm not talking only about these days. If Jeremiah acknowledges and warns about wrong prophets, how exactly is it certain that any of the prophets in the Bible were actually receiving the word of God (or same god even, assuming there were many of them)? Obviously an established religion doesn't want people to come and rock the boat with newly revealed divine information, so they quite often "close the door" so to speak, to keep established dogma safe from change since change might be a bit unconvincing: How is it that now this is the truth but yesteryear it was a lie? Even the most uneducated peons would start asking questions at that point. Therefore main religions can't really change, they can just undergo reformations which tend to be bloody and profound.
And yes, if you read between the lines you might notice some marxist undertones there. Not that I would have much in common with him, but I do view religions first and foremost as mass control devices for the (religious) authorities. Islam being the worst in this time because religious authorities there tend to also have significant secular power, which is unfortunate. Roman Catholic Church used to be like that but after the reformation they kidna lost their grasp on secular politics (which allowed growth of secular philosophy and enabled Europe to develope much faster than the rest of the world in terms of natural sciences and technology). Of course, cults are the culmination of control over members, and go way beyond any religion in that sense. In fact I would say that the only thing that separates a cult from religion is the amount of control it demands from its members, and the amount of those members.
Re: Flood.
It is widely accepted historical consensus that some kind of cataclysmic flood event did happen at some point in the history of Middle-East or close by, and that some records of it have survived to find their ways to Gilgamesh epic and the Bible, and other records as well. This, however, does not mean that everything in the Bible would be equally accurate historically, and it means even less considering the source of the text being divine or not.
There certainly never was a flood of the magnitude it is described in the Bible engulfing the whole world in several kilometres of water, so the accuracy of the details is quite suspicious. Flash floods aren't entirely uncommon, although it is possible that the flood in question might have been quite unique, mainly the filling of the basin of the Black Sea when the Strait of Bosphorus was formed (it's the closest thing that would match the description of incredibly widespread catastrophic flood, but there are doubts that it was the case).
Something regarding abiogenesis and formation of life: Ever heard of the anthropic principle? It basically says that the universe is as we observe it to be, because it's the only way it
can be in order to produce sentient life of our kind. It doesn't say that universe was designed or made to be suitable of generating the life as we know it, and us, it says that if the Universe had been a bit different, we wouldn't have developed at all. In a multiverse interpretation of quantum physics this means that formation of life is not a big wonder at all and that there are almost infinite amounts of alternate realities where life can never spontaneously emerge because of those worlds lack the prerequisites for, say, molecules to form long chains in the way carbon does. No long molecules, no proteins, no organic life.
It is entirely possible that we are here because universe happens to be the way it is, without no divine (or infernal for that matter) entities affecting the processes of Universe.
As a slightly related tangent, the ancient Greeks had a very interesting way of putting religious and mundane world together; they called it
cosmos; basically translates as "place of order". Despite their polytheistic beliefs of a pantheon of strong beings living in Olympos and affecting the life and times of people on Earth, they all lived in cosmos and they all had to obey the same basic cosmic rules. We would call them laws of nature or physics. This view of world, incidentally, was probably what triggered the surge in natural philosophy in ancient Greek; other places were still using the Gods of the Holes to explain everything, while the Greeks figured that even their Gods were part of the same reality and thus couldn't simply be attached to every unknown thing. Or at least the people who dedicated their lives to thinking these things through did.
