Kite by learning to orbwalk . What I do is use "a" key-left click (which has it so you attack whatever is closest to your cursor, so you don't have to click on someone directly). Shift-right click also works.
Deal with assassins best by having summoner spells up if you're an immobile ADC, or not wasting your mobility (to cs, for example) if you're a mobile ADC. Getting Ionian Boots/Distortion enchantment allow you to have summoner spells up more often, but I rarely go this route. Building lifesteal earlier, and building a defensive item such as Banshee's or Randuin's can help. I usually only build a defensive item in extreme cases.
If there is a big wave on one of the side lanes, you should go clear it for the gold and the pressure it'll place on the enemy tower. As a general rule, don't wander past the halfway point of a lane alone without vision.
Solo carry as an ADC is sorta hard because you rely on your team to an extent. Try taking bot tower ASAP and grouping mid to take towers. Focus on not dying in teamfights. Remember as an ADC, your most important contribution to the team is you do the most dmg to objectives! Your team won't be able to take objectives as easily after a teamfight if you die.