Rosin is also used on violin bows to increase friction, and it’s the white powder you’ll see gymnasts and baseball pitchers apply to their hands to improve grip.
Rosin vapour is a lung irritant, so avoid breathing it by using a fume extractor, and for some people it can cause contact dermatitis.
Yes it’s horribly sticky, that’s the worst part about it really. Isopropyl alcohol will dissolve it.
Other technologies like glues and crimping have their uses but are less reliable, higher resistance, or difficult to automate.
This may change but there’s little demand. Glues have lower conductivity and are harder to remove, mechanical connectors are bulky and not as strong.
If you’re applying fluxed solder directly there’s not much point applying separate flux to clean metal. Of course the flux will boil off pretty quickly so you need to use extra if you’re doing something where the solder wire doesn’t directly touch the components, or if the metal is old or previously soldered.
The only advantage to non-fluxed solder for most hobbyists is being able to choose your flux, but for most of us rosin is fine and fairly non-toxic.
But besides breadboards you're kinda stuck with facilitating a clean soldering setup, which is fairly easy - if you're really worried build a gloved-box. I just wear a respirator and open a window