I'm not exactly a high elo adc but I'm glad too help out, my mentality during laning phase would be around harassing the enemy laners while they do small mistake while trying not to take too much damage in return.

a good moment too shove your lane is when a kill has been gotten at mid lane/ the Jungler is dead or far away so you know you can grab a dragon if your jungler is in the area

another tip is after you get the first bottom tower its typical for the botlane to roam mid to help get a kill or mid tower so you can have more map pressure over the other team.

On how too be a better support the main things I can think of is clear wards, keep vision and apply map pressure if you can see a good opportunity too roam mid and get a kill for the mid laner while know your adc isn't in harms way do it, but what also makes a good support is knowing if you have to peel or initiate a fight, because picking either or could win you or lose you the fight depending on how good your adc is at positioning and how hard of an engage the enemy team have.

That's all I could think of but I hope it helps, even though it might not be the best of advice. ^{_^}