In the back of the owners manual is the wiring diagram
You will see in the start position the power goes from the key switch ( S terminal ) to the PTO switch to both lap bars to the brake switch to the solenoid
If the 20A fuse blows every time you turn the key to S then you have a dead short some where in that circuit.
The other possibility is you have installed the battery backwards.
The fuse melting is because you have a bad connection at the fuse holder.
Cut it off & replace it with a waterproof one or keep it greased to prevent water corroding the
wire under the crimp.
A photo of the solenoid would be very helpful as it is possible to conneect them so they are a dead short.