I obviously don't know the answers since I wasn't there and the Bible doesn't provide the details. Proposals that I've heard that make the most sense are:
Where did all the water go after the flood?
Prior to the Flood the Earth had a fairly mild terrain without high mountains and deep sea trenches. During/After the Flood - when "...all the fountains of the great deep broken up, and the windows of heaven were opened" - mountain peaks rose up, and sea trenches were created in the oceans beds -- thus allowing a recepticle for the water that covered the surface of the Earth.
What did Noah feed to the lions and tigers during his voyage? As I understand it both have hearty appetites.
One proposal is that most of the animals went into 'hibernate mode'... I know if I had been on board the last ship on Earth, while 'terra firma' was getting ripped up and covered with water I'd probably been in a 'wake me when its over mode' as well...
God Bless.