Wiring getting hot and fuses popping is too high current and / or short circuit fault,
You may have two problems here, firstly a dead short on the indicator circuit popping fuses instantly. Short circuit = live finds a low resistance 'earth/ground fault , and a bigger current flows melting the fuse within a second or two - the resistance of the bulbs/load limits this current in normal use)
Secondly, bad wiring causing the main ignition power feed to get warm - shouldn't ever happen. Block connector in headlight getting warm points to a dodgy connector there, or bad ignition switch or fusebox. Old z1000 fuseboxes can be a problem here.
Probing this with a voltmeter expecting it to be down a volt at the end of the dodgy wire won't happen, as you need to draw a current through the high resistance of the bad wire/connection, more than a meter will do.
So a dodgy live circuit would test meter at perfect battery voltage, but when connected a bulb or other load would glow dim.
Checking resistances with a meter on the circuit from battery to fusebox, to igniton switch and back to fusebox (the main fuse powers all the others on the later z1000) might be where the problem is. Too much current draw probably caused by caused by a voltage drop (resistance) somewhere in circuit. It gets hot as the load needs to draw a higher current to compensate for reduced voltage. Heating in a wire is proportional to current squared, so a small difference here makes a big difference in wires getting hot.
Do the main wiring heating problem first , then look for indicator fault.