The fuel hose is the one I've circled in green and it attaches to the bottom of the fuel pump (the white plastic part).
There's a black plastic cap that has to be unclipped before the hose can be removed.
The open ended hose on the left side of the tank (that you circled in red) is the overflow, the one on the right hand side (at the top left of the picture) is the breather that stops a vacuum lock forming when the fuel pump pushes petrol through to the engine.
They run down through the frame at the back of the engine and, if you can be bothered, there's a square bracket at the bottom of the centre stand that they can feed through to keep them tidy.
Just make sure that, when you lower the tank, neither is caught or pinched and you'll be fine.