The cables can be secured to the frame using black zip ties or even black insulation tape, but you need to make sure that the battery connections on the contactor are safely insulated.
I recommend using rubber/plastic boots to completely enclose the exposed metal terminals as shown below:
I would also rotate the lower terminal and place the locking washer between the terminal and the contactor so that it is spaced even further away from the frame, but don't position it too close to the contactor's ground connection, or that could result in a short circuit too.
The contactor should not need to be mounted on rubber grommets as the mounting bracket should already be electrically isolated, and very little vibration
(if any) will be produced by the electric motor.
Regarding the seat, good results can be achieved by constructing the basic shape from cardboard and then apply layers of fibreglass over the top to achieve the required strength.
After some body filler and a lot of sanding you end up with a surface that can then be painted to match the tank and side panels etc.
Here are the before and after pictures of my brother's first moped taken back in 1980:
The above image was scanned from some old slides which were developed nearly 39 years ago, hence the strange colours.
The slide showing a close up of the mural on the top of the petrol tank seems to have been relatively unaffected:
Exposed groups of cables can be bound together using black PVC loom tape, which is similar to black PVC insulation tape but without the adhesive backing.
Alan