All roles need to know how to last hit, last hitting should not be a skill just for 1 position players it's a skill in MOBA in general. If you're a support and you have a free lane to farm you BETTER get those 5 last hits when you have a chance.
Knowing how to carry is far more advance then people think it is. The decision making, time management, map awareness, risk mangement have to be spot on, do not blame your supports if you get ganked because there's no ward there, if you watch pro games the top carry players never overpush and know when to hide in the fog when everyone is missing regardless if there are wards up.
Playing support is about being able to position and making stuff happen with nothing. I see too many 4/5 position players afraid of dying (ie Sandking not wanting to go in to epi stun because he will die), you have to understand it's your role to throw yourself at your enemy to make stuff happen, learn to position yourself in team fights and always understand if you died but your 1/2 position player got the kills its fine.
Best way to play better is always to play all roles, understand how each role works and that way you can play against it better, once you become a better support you will 100% be a better carry also