Thresh has a very high skill requirement and require a lot of knowledge with positionning, team synergy, usage of CC and yada yada. I don't know how well you do with Thresh but he's rarely the best pick for someone trying to improve from bronze.
Soraka is 150% reliant on her team to do anything and the only carry you can do with her is to reduce the amount of gold the enemy get. Just like Janna except you can't prevent damage taken by your team or cover for their bad positionning.
Alistar, Nautilus and Janna are all great support champions to start with.
As for your questions:
- You don't. At least not literally. You don't "carry" a game as a support, you allow your teammates to carry and/or you negate the enemy carrying.
- Be versatile. One of the most important part of the game happens in champ select. Play the champion that synergize the best with your team and which can screw up the enemy hard. You have a Jhin for ADC but they have a Zed or Talon mid? Play Alistar. The enemy has a very hard engage team? Play Janna. You got a Ashe ADC? Play Leona!!!
- You need at least a backup role for the rare case you don't get support, but you can very well rank up as support only. I only support (minus the rare times I mid) and I'm climbing rather quickly.
My advice?
There is nothing stronger than countering an opponent.
Cockblocking, zoning, disengaging, sustaining, map pressure, map coverage, etc.
They are all good ways to counter. You just need to play to your team strength and capitalize on your enemy weaknesses.
For example, Draven is a bully but he is extremely vulnerable to hard CC, snares and displacement. When against, depending on the enemy support, an Alistar, Blitzcrank or Nautilus can easily screw him up. A Karma can also work well if his support is a bully without sustain or early hard engage like an Annie or Brand.
Always ask your ADC what he's gonna play in champ select and if you are first or second pick, go with a safe champion like Alistar or Janna.
Edit: Another advice...
Time your abilities.
Do not exhaust an enemy that is already CCed or that isn't actively doing damage, unless it's the only way you have left to keep them from escaping and secure the kill or if they are going to kill an ally if you don't use it for the snare.
If you play Nautilus, don't ult while the target is already locked down by your passive root. Wait for them to attempt an escape, to engage or to stop them from dealing damage to your carry.
Losing even 0.5s of CC because you use multiple at the same time can be fatal or mean that the enemy will escape with only a sliver of health left.
Edit 2: Don't get caught. Dying means the enemy team get gold and you lose precious time without any XP gain in a role that is already XP starved.
Learn how to play the pink ward game and when it is safe to make an attempt at destroying an enemy pink ward. Always be aware of where the enemy team is on the map or where the enemy jungler was last seen and when.