add to 1. main reason to use them for many people : "because they are cute" :-) and imho they fill the gap between using belts for local distribution (eg between a depot and the assemblers of a single assembly line) and any more distant connection like a main bus. they don't collide with each other and thus a huge number can use the same narrow road at the same time, instead of a main bus with 8, 12, or maybe even 64+ belts :-)
they might even be usable instead of short and medium trains connections since they can transport up to 6 stacks per drone, load and unload much faster and in much more compact loading/unloading stations, and also require only a road instead of double train tracks with signals, crossings and all that related stuff.
you also shouldn't only look at the speed of drones and bots, but at their throughput in some specific setup. for transporting a single satellite, a bot may be better suited, but to transport 600 plates or 1200 science bottels or wires, you need only a single drone instead of hundreds of bots (if researched to max bonus). there are lots of new challenges involved when using this new different method of transport.
add to 3. : i lost quite a few drones when they kept running through acid puddles from spitters. thus roads probably should be protected somehow, eg by a row of powerpoles, each with a laser and a repair turret. @Klonan: maybe the acid resistance of drones should be improved a bit to avoid them running into those deadly lakes that spitters sometimes make? or would that make them overpowered?
btw: https://mods.factorio.com/mod/Repair_Turret is another mod by Klonan
add to 7. : roads MAY be as narrow as a single tile, but shouldn't since pathfinding is optimized to work better (less UPS) when based on an internal 2x2 grid (not to be confused with the 2x2 grid to place rail tracks), and thus when roads are at least 2 tiles wide.
add to 8. : by default (when using only this mod) they use petrol gas as fuel, but there are also some mods already that change this to use either steam or special drone-fuel instead so that this mod can already be used right in the earliest game. and Klonan himself has added mod options to change the type of fuel, so that you theoretically can switch to using any fluid as fuel, including acid or vanilla water :-) in addition and afaik the tooltip of one of the options ("fuel usage" ?) says that setting it to 0 disables use of fuel.
add to 9. : if you meant "to the logistic network", the answer is "yes and no" ... yes for suppliers (and new items in the last updates that i only installed just now and haven't tested yet), and no (at least not directly) for requesters, mining depots and similar which are not based on chests but are implemented completely differently.