I don't have a photo, but the your undersink plumbing may be correct, as Scamp
(and others) does use hose and clamps.
There are really three systems under there, tank water, city water and drain.
The tank water is a tube going into the bottom of the manual pump faucet (look closely at the base to learn which lever position keeps water in the tube between uses and which allows the tube to drain back to the tank).
The city water is a regular sink faucet connected to a wall fitting that goes outside and allows a hose from an outside source to be connected.
Presuming you don't have a full bath with gray tank, the sink drain connects to a wall fitting that empties right outside. What I have done for my gray water is connect a short piece of hose to the fitting, with the other end cut off. I took a laundry detergent jug, cut out the internal spout and drilled a hole in the cap just barely larger than the hose. I set the jug on the ground, put the hose in and the fit is tight enough that the little bugs don't gather. Empty the jug down the sewer hole or carry to toilet.
I don't know where you plan to put the bike, but the rear bumper of the egg is not a good idea. Hanging weight
as far back as possible on a trailer creates a sway problem... Also the bumper is not intended to carry vertical weight