I tend to believe that the earlier accounts of Genesis tend to answer theological questions and set up the mindset passed down to them, through "inspired mythology" in Via Crucis' terms.
I'll answer your questions with the idea that the flood actually happened, but was local to a people in a shallow area below sea level.
Approximately what year(s) did the flood occur in?
Perhaps 4000 B.C.
How long did the flood last?
roughly a year ("source:"
How Long Did the Flood Last? | Noah's Ark: Beyond Flannelgraph)
Considering the area must have been perhaps 20 feet below sea level (as the waters covered the nearest "hills" for 20 feet)
Were any areas of land accessible during the flood?
Yes; assuming that the area was in the Mediterranean sea area (and the flood occurred due to the strait of Gibraltar opening up, as one theory has it). The thing is, for where Noah may have been, to walk there would have been futile/fatal.
Where did Noah build the ark?
On land most likely near where his house/tent/abode was.
" The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits."
A cubit may range from 18 to 21 inches, some fix it at 18.
With the curvature of contemporary nautical craft, and in standard vector notation (length, width, height),
it may range from (450, 75, 45)ft to (525, 87.5, 52.5)ft.
How many different species of animals were taken aboard the ark?
An indefinite number of pairs of "two of all kinds on the earth."
How were the animals gathered up?
From Noah's flocks and herds that he tended, along with any other animals he may have wanted to salvage.
How many humans were on the ark with Noah?
I believe 8 people, Noah, his wife, his three sons, and their wives. The actual amount may vary depending on if he had more sons, if the sons could have more than one wife, and if he had daughters who were also taken aboard but not mentioned. So 8 people were revealed at the least.
Did any humans other than those on the ark survive the flood?
Those who weren't in that geographic location.
What modern day geographic region did Noah sail in the ark?
I believe it'd be somewhere in the Mediterranean or somewhere in the ancient Asia Minor. The actual location is never really mentioned, hence its mythological nature.
How long was Noah stranded in the ark with the animals?
Probably the whole year unless the ark made it to land before then.
How far in advance of the flood did Noah begin the construction of the ark?
For as long as it took Noah to construct the ark, perhaps the best case for its mythological nature.
What prompted Noah to construct an ark?
God's informing Noah of clearing the area out and salvaging him.
Was the ark constructed on land or in water?
On land.
If the ark was constructed on land, how was it moved to the water?
The water came to it, such as a large surge of tsunamic water or geographic such as the Strait of Gibraltar opening up.
Where did the water of the flood come from?
If in the Mediterranean, then the Atlantic Ocean; if in Asia Minor, then due to an unusually large flooding of the major rivers or a large tsunamic surge.
How did the water of the flood recede?
relative to the ark landing far or a great distance from its beginning location, I don't know. Relative to the cease of the large river output (perhaps due to the melting waters of the end of the last ice age, so pushing the time further back), I don't know.