hi
nasty its melted coz its was either loose and arked as you hit bumps on the road or some think has been done to cause the damage like wiring
right lets sort this fan out by trying this
1) remove the plug which connects the fan up, should be down on the left
2) if you have a multi meter or light tester connect it up to this connection and bridge the fan temp switch again this will find out if the fans the problem but give the connectors a good clean as they corrode alot as being at the front, do both male/female with pick/wd40
3) run a neg and positive to the fan with engine off not on as voltage higher this will definately tell you if its the wiring by doing the last 2 stages
if it is found that the wiring is at fault it may be linked to the fuse box by the sounds of it
right the lights
fact is if its melted the relay holder the heat would of damaged the contacts so just rewiring it from the bottom may not solve it unless you can replace the connectors inside
personaly if you do the tests above and its the wiring with regards the fan then i would be inclined to replace the fuse box with a good one from a breakers ect ect as this may be causing both problems

it depends on how you want to fix the problems as you can buy a fan controler which goes into a water line and comes with its own wiring and relay and is totaly independent of your engine bay wiring and you can get them with a varible one which means you can control when the fan comes on ie at a certain temp
same for the lights you can rewire them independently and still use your switches or new ones
but if you have problems now with the fusebox whos not to say more will crop up soon
sorry for the grim news
mark2