To be honest, even if 3 losses in a row looks like a cause for concern (especially in ranked) if you play this game regularly chances are you'll eventually hit a losing streak. If you come back sometime afterwards it means you're still deserving of the rank you have or better.
With that out of the way, I'm also trying to learn marksmen to help in my supporting ability, to fill in the role if/when no one wants it (which has so far only happened this season I think) and to generally learn mechanical skills like CS and positioning better as the key role on my team.
One thing I've noticed since I started learning ADC is that I tend to lose games as 
and win games as 
. I think this is for two reasons:
-
Lucian has a shorter autoattack range, meaning he can't harass from a distance and is generally riskier. Lucian is also more of a lane bully than a DPS carry, while Tristana can come back later and even take objectives without many kills.
-
I understand how to build Tristana a lot better than I do Lucian. With Lucian I've tried raw damage, mana, CDR, you name it; I still can't consistently perform well with him. With Tristana I know she doesn't need more than 1 attack speed item, so I'm free to build raw damage and tankiness or CDR.
Judging by your match history, you seem to play a variety of marksmen. Your K/D/A is consistently good with Vayne, which isn't a surprise since so many people hate her. I also see that you rush Infinity Edge or Bloodthirster and Berserker's Greaves almost every game. You probably should reconsider how you build items and when.
For example, one game you built a Last Whisper against a burst-heavy team with only one really tanky character. In that situation a good counterbuild would have included Mercurial Scimitar instead, which gives magic resist and an active ability that can help you break CC and escape their fighters. Remember, items are extremely important to marksmen, so how you build will change how you play and with who you will effective against.
Also, a little defense can go a long way. If you find yourself outmatched by the enemy marksman or other AD scaling champion, consider Ninja Tabi since it directly weakens autoattacks and let's you trade with them. Again, Mercurial Scimitar helps against CC-heavy champions and magic damage dealers.
Second, as far as positioning goes, it depends on the matchup. Obviously, when against hook champions you'll want to hide behind minions and wait for them to blow their spells (which is easy to do with Sivir). Against healers you usually want to be hyper-aggressive and bring them down to where they can't get up and dominate from there. Against tank supports, target the marksman instead (if possible) or wait for an opportunity to hit, such as a gank. Tanks will be easier to fight when you get counter items like Last Whisper or Black Cleaver (if you swing that way).
Also, in teamfights, you should generally try to hit the squishiest enemy in range without getting hit yourself. Don't try to go too far out of your way to get to lower health enemies, what matters is doing constant damage for as long as possible without dying. That doesn't mean you shouldn't attack squishies, just that doing so in the middle of the enemies is a LOT more dangerous than hitting a fighter in the middle of your team, then moving on to the fleeing squishies.
Against assassins, you don't want to be near assassins. This is why tanks matter for your team, since they can help lock them down for you to kill. If you see one jump on you, either immediately use your mobility spells, hide in a bush, or just search for a safe spot with allies. You almost never want to be alone unless it's to get a dragon while all three enemy inhibitors are down.
I hope all this helps. This is what I've gathered so far playing as a marksman, and I'm looking to improve myself.
