#1, #2 and #3, read Fred's guide: https://www.mopedarmy.com/wiki/Fred%27s_Guide
#4, get a new spark plug. check spark. if no spark still, disconnect the kill wire from the CDI, essentially hotwiring it, this bypasses all switches so you can see if that's the trouble. it's a red wire on the CDI box (looks like theres 2 red wires, i mean the one going to the harness and up to the ignition switch), just disconnect it (snip it if you have to and splice it back later)
#5) if still no spark, keep red disconnected, check the other red and white for continuity from stator to the CDI box, and check blue from the box to the HT coil. spin it with a drill; chuck up a socket for the flywheel nut in a drill to turn it over while checking spark. check power on those wires. double check all the grounds with a multimeter too.
#6) If it's getting power in on the red from stator and at least tiny measurable pulses from the trigger, white from the stator, but nothing outta the CDI box on blue, and you know grounds are OK, then try new box. check the pinout, i strongly suspect it's a "5-pin cdi box" and almost any 5 pin 2 stroke CDI box will work, theyre cheap and easily found on ebay and amazon, usually including a HT coil too., you'll have to figure out wiring because wire colors wont match, but it's explained here: https://www.mopedarmy.com/wiki/Hobbit_CDI_Wiring different bike but same info applies to you. also here: https://www.mopedarmy.com/wiki/Performance_racing_CDI
#7) IF you can get it to spark, then worry about the carb. I guarantee it'll be easier to repair the one on there, because it'll already be tuned to the bike. there are FAR FAR less parts than car carbs, and knowing how to clean it quick on the fly can be a big help. you shouldnt need mre than a phillips and a flathead and a clean space to put everything. that carb looks like a clamp-on clone of the mikuni VM12 (probably 12 anyway). There are zillions of minutely different versions of those carbs, but if you need to, a clamp-on VM12 should work, like the ones yamaha used on the QT50's and PW50s, which were popular enough to have replacements available. It's not identical but it doesnt need to be if it fits the clamp. you will definitely need to buy a range of jets and swap them until it's working right, so even if you buy new you will 100% need to be disassembling and reassembling it to swap jets. check out this QT50 VM12 for comparison:
Beyond that it looks like the base of that clutch is blued pretty badly. I dont know the specifics of that engine (hero is not a very common engine in the moped world and an oddball mashup clone of several others), but i'd suspect it's got maybe a starter clutch under there that's always sortof stuck on and was just rubbing and scorching that bell.