First, your battery is most likely trashed. You need either a good fully charged battery or jumper a car battery to the bike battery: be SUPER CAREFUL not to connect the jump battery reversed!
The fuseholder heating isn't too surprising. The fuse contacts once had a plating that's long gone by now, so connection to the fuse will be less than perfect - plus once overheated the contacts lose their springiness. You should replace the fuse holder, I think Hondaman sells a type that mounts and plugs in just like the original but uses the modern minifuses common in cars for a decade or three.
The headlight - not sure what's up: if you turn it on and the battery voltage dies then something is connected to the switch. Is it the headlight, or has the wiring harness developed shorts (not unlikely with foiled fuses as overcurrent can melt wire insulation)?
Foiling fuses is a very bad idea. Try soldering wires to a tail lamp bulb and putting that in place of the fuse. A short will light the bulb full bright, just the instrument lights will give a dim glow, and the headlight will glow dim but the test light will be bright.
The wiring is generally simple: all bike power goes through the MAIN fuse, the HEAD and TAIL fuses are after the MAIN fuse. There's some weirdness for the PARK key position... the tail light will light in PARK with the TAIL fuse removed. With key ON the black wire is powered and all loads draw through a black wire, the black wire connects to the HEAD and TAIL fuses. Some weirdness there as well, if the TAIL fuse has no power and you don't have a headlight on/off switch there may be a jumper missing that replaces that switch for always-on headlight locales.
The headlight power is switched in the start button, so that the electrical load is minimized when electric starting. A black power wire goes to the start button, connecting to the headlight circuit when not pressed but disconnecting that and connecting power to the starter solenoid when pressed.
So in essence: get a good battery and have a plan for testing. Check that power is at the MAIN fuse - both ends. Check that power is on the black wire with key ON (you should have the kill switch as STOP for all this testing to reduce load and avoid overheating one or both coils with engine stopped). Check for power (key ON) at the MAIN and TAIL fuse. Check for power at the headlight plug, there's a green wire (ground) and two power wires to the socket - for hi and lo beams.
If you have power at these places then the headlight should work. No? The starter button is a major cause, it really wasn't designed for the full headlight power and aftermarket higher wattage bulbs are death for them. If it has failed that may explain your lack of electric start too. Replacement switchpods are available but either disabling the headlight cutout by bypassing the starter button switch - or adding a headlight power relay - is advised. You can put a miniature SPST button switch in the housing to replace the original starter button with either the bypass or the relay. The switch itself is really not repairable - the plastic housing turns to crap and internal parts were never available, just the entire pods.
