Hey man! i'll chime in here and give you some of the basic tips i learned from playing bot lane as well as link you some general videos that will help you become a better ad.
So i'll start off with some specific things that you said in your post and try to explain them to you.
but it always been so hard to carry as an ADC. Especially in teamfight, the enemy just literally throw everything on my face
Naturally you know from playing other roles you want to go after the AD carry. AD carry does a ton of damage and is scary at almost any point in the game. So in team fights this is what you want to do.
- stay at max attack range unless your team is winning the fight, at that point you can walk up but never get in melee range.
- wait for big enemy cool downs to be used on other champions
- Never dash IN, always dash diagonally or sideways
- Try to work around a teamfight in a circle rather than going straight through the diameter of the team fight
- if you don't have flash up always stay about AA+flash range away from a bruiser or someone diving you
I'm going to highlight some main points here that i think you should really take into consideration. The most important thing is to wait for enemy cd's to go on cool down. If you walk into range of Vi she WILL ultimate you. If you walk into range of irelia's gap close she will use it on you. If you stay along the outside of the team fight throwing spells in but not auto attacking, you will still be doing SOME damage, but more importantly you are not being focused. Once the team fight starts people generally blow all their spells at the beginning and at that point you are free to come in and pump out damage. It should not take longer than 2 seconds after the team fight starts where you should be safe to enter it. If you are playing champions like lucian or varus who can do a ton of damage from afar this works best. NEVER dash IN to a team fight. Always dash diagonally and sideways. This is because 1) you don't want to get into melee range 2) you want to stay at max range while positioning better in a team fight 3) you don't want to dash completely out of a team fight and walk all the way back into the team fight. Another thing i didn't mention above but is super important is csing. you said you had average csing but you really want to be able to cs perfectly. Go in a custom game with no runes no masteries and no items pick vlad and try to get 100 cs @ 10 minutes. If you can cs perfectly it doesn't matter if you have kills or not (until really high elo) The most important tip i can give you is IT'S ALWAYS BETTER TO BE MORE AGGRESSIVE AND TONE IT DOWN RATHER THAN BEING TO PASSIVE AND BECOME MORE AGGRESSIVE always go for the trades and learn from each trade if it was successful or not and WHY.
** tips for varus**
- Start Hail of Arrows (E) --> Blight (W) --> at this point you can either take 1 more point in E or max Q. You take E if you need to trade better and Q in any other scenario.
- Always Auto Hail of arrows Auto attack. ( you should almost always hit it)
- You should almost never just "throw" ultimate out, You need ATLEAST 1 stack of blight
- Buy health and mana pots because you use a lot of spells
- If you max Q try always use it at max charge up
- use blight as much as you can, makes trading more effective
** Tips for Cait**
- You are the scariest at level 1, pressure A LOT
- always stay at max range
- Push the wave because it's easy to harass them while they try to cs
- Always have mana for net
- traps give you a ton of pressure use them!
To finish up i'll give you a few more tips then post a link
- Always auto Spell Auto
- You generally always want to push the wave into the enemy turret before recalling because it makes the wave push back towards you. This denies them xp and puts wave position in your favor
- The only time you don't want to push the wave into their turret is if it's already pushing towards you. You will end up denying more cs than pushing it into the turret.
- Always take an auto on a champion rather than a cs.
- pushing the wave takes pressure off the map, and puts pressure on their bot lane. ( alot of people have trouble csing under turret AND you can harass pretty easily.
- ward pls.
- Hide in bushes and surprise attack. You usually always win these.
https://www.youtube.com/watch?v=6ywhB-2h2AE&list=PL9RdXhXESRJx6Iur1Faq-Ai82vgWej_fB