Is it legal to build your own plane and fly it? Is it legal to build and fly your own airplane? This essentially leads to two central questions: Will the FAA even let you build and fly your own airplane?, and Will there need to be inspections and testing records to certify it as flightworthy and legal before being able to fly it?
Say I built my own plane, a large plane. 3 Propellers powering the plane. Amphibious, can land and take off on a runway or on the water. It's red, if this makes any real difference. And it is built to support 2 people and is supposed to be able to fly for up to 1 week without refueling. That being said, if the plane crashes it'll cause quite some damage. And to fly for 1 week supporting 2 people and quite a lot of cargo in the form of food and other essentials, the airplane is loaded with fuel.
If I know the plane floats on the water, could I fly it in an unpopulated area in short testing runs, or is that considered illegal? This also brings the question, Is there is a limit to how much fuel a plane can legally carry in a single flight? Any help would be much appreciated.
Yes, it's legal. The FAA has an amateur-built aircraft homepage with links to regulations, guidance etc.
It's also very common. The Experimental Aircraft Association has a lot of resources too.