Yes I believe that all three people physically existed, and I believe that the stuff written about them in the bible is true. I also believe that a worldwide flood existed. Though it may seem implausible for their to be a world wide flood, God certainly could do it, if you, like me, believe that God is all powerful. Let me point out that Noah brought seven clean animals of each kind of animal and two unclean animals of each kind of animal on the ark, according to the bible, so there weren't just a couple of animals on the earth to start out after the flood. As for the size of the ark, well God gave Noah 120 years to build the ark, so it naturally should have been quite large according to the number of years it took to complete it. Also, though feeding and maintaining all of these animals once on the ark seems implausible, God can work miracles (according to the bible, he gave the israelites bread from heaven in the wilderness and he fed 5000 people with 5 loaves of bread and 2 fish), so it seems logical that he would be able to provide Noah with a way of feeding all the animals.
As for the reason behind the flood, here's something very interesting in the bible that you might not have known even if you were familiar with the bible. Genesis 6:1-2 states "Now it came to pass, when men began to multiply on the face of the earth, and daughters were born to them, that the sons of God (meaning the fallen angels from heaven who sided with the devil, because the same phrase appears again later in the bible obviously referring to the devil's angels) saw the daughters of men, that they were beautiful, and they took wives for themselves of all whom they chose." Verse four goes on to say, "There were giants on the earth in those days, and also afterward, when the sons of God came in to the daughters of men and they bore children to them. Those were the mighty men who were of old, men of renown." What this means is that the fallen angels, the angels of the devil, actually took women from the earth as wives and bore giants and the like to them. So God meant the flood to cleanse the earth of it's impurities suffered because of the deeds of these fallen angels, and to start the earth anew. That is one reason for God to flood the earth, another reason being that man was disobeying God in those days.
Also, explain to me how scientists have found fossils of sea creatures on the tops of mountains. I was told that this phenomenon was attributed to earthquakes causing mountains, but this is something interesting to look at.
I'm sorry that this was so long, and I'm sure many of you do not agree with anything I said, but this is my personal view on the issue of the flood.