You don't have to be a 1 trick pony but should limit yourself to 2 maybe 3 champions in two roles. Figure out your 2 best roles or roles you want to learn and only queue up as those. Play same champs over & over so you get better with that champ and learn match ups. I suggest not playing support unless you feel really confident in playing it. You can carry as support, but its hard to do in bronze unless you know what you doing.
Focus on csing in lane and getting some poke on enemy champion while staying safe. Keep eyes on map to be aware of enemy jungler. In bronze players are generally really weak at staying safe in lane, so I am usually able to kill my lane opponent a couple of times to get ahead. Once you have a lead then snowball the game by ganking other lanes where the enemy is out of position. Best place to gank is usually bot since that is where most players are.
Its hard to put into words of how to get out of bronze without showing someone. I am not very good, but I know the game well enough to carry in bronze fairly easily. Its really just about getting ahead and staying ahead. People love team death match in bronze so if you are strong enough to kill 2-3 enemy players each team fight then winning games usually are easy since the other 4 players on your team just have to focus on killing the remaining 2-3 enemy champions.
Honestly man your cs/game levels look pretty low so that would be a good thing to focus on. You can get to silver with last hitting poorly, but it would really help you level if you get better at it first. I am pretty poor at csing but I am good enough at it to match the average gold player. So when I am in a bronze game I am usuallyr ahead of most the enemy laners and my teammates in cs which means more items for me. On top of that I usually have most kills so now my gold lead is waaayyy beyond that of other players in the game so I have by far the most influence. And since I know the game better than my bronze teammates and enemy players, I will be able to carry more games to victory than defeat resulting in ranking up.
Here is an example of how I would play 
mid in bronze (well all ranks but this is what usually happens in bronze for me based on past experience). I start mid and freeze lane while csing. Most bronze laners don't freeze and just hit minions so the lane keeps pushing. This allows me to farm safely while leaving my enemy vulnerable for ganks. I will try to hit enemy with poke as much as possible while avoiding any skill shots they have. Sometimes the enemy will go really ham by like level 2-3 and I will get a kill. If not, then I will make sure to ensure a kill by level 6 when I get tibbers. Most games I will have 2 kills by the time I hit 6. I shove wave to turret, back and buy then head back mid. Now that I have a lead the enemy laner has to play safe or I will kill them every time my ult is up. I will also continue to look bot to see if the enemy bot lane is out of position for me to sneak around and gank. If I see they on our side of the river I will head bot and most likely pickup a double kill. Maybe I see the enemy jungler heading down there on mini map so I go down to save my bot lane and turn fight and we end up getting 3 kills. Then I head back mid and continue csing and pushing lane. I pay attention to the map and see if enemy bot lane gets out of position again or if the enemy jungler is out of position and easy for me to gank. Continue to do this over & over until teams start grouping. If you do this successfully you most likely should not get too far behind in cs and be ahead in kills. So now I look for an opportunity to flash tibs bomb the enemy carries. A lot of times bronze players are poor at positioning so getting a 3-4 person tibs ult especially on their mid and adc is usually pretty easy. I insta kill them and team picks up killing the rest of the enemy team. The shitty thing is people never seem to want to push in bronze so its hard to get a game to end before 40 mins. And even if you are fed its hard to sometimes win late game before its 45 mins in, enemy team is catching up in items and death timers so long.
The thing is though you don't have to have 20 kills a game to carry in bronze. There are times I get many kills and carrying is easy but other times one of my teammates might get fed instead. And this is the case for the game as whole. Learning when to engage and when to run is important along with having map awareness of where the enemy is. You can be 50-0 with 400 cs but if you blindly walk into the enemy team alone and die you probably lost your team the game or at least baron or elder dragon. This already too long but gong to try and make a list of things that go through my head (I am only gold 4-5 player so keep in mind I am not close to pro) in an average game.
- Do I feel confident in my lane matchup? I.e. I feel confident in match up = playing more aggressive. Unsure or feel its a poor match up for me? = Play safe,freeze lane, wait for opportunity/opponent to make mistakes.
- Where is the enemy jungler? Is the enemy jungler
and I only really have to worry about ganks when he 6? Or is it 
and be aware of ganks at pretty much any level?
- Am I ahead of my lane opponent? If yes, play more aggressive. behind play passive.
- Lane opponent missing? If I know or feel they ganking another lane and I can help follow and try to counter gank. If I feel they too far ahead or I can't help, push lane.
- enemy team grouping around dragon? Try and stop and fight if jungle and team want to fight it. Otherwise keep farming/pushing lane.
- My teammates mid saving mid turret but no one bot or top to stop minion wave from pushing? Head to that lane and clear wave and push lane. Hopefully team does not engage if its a 4v5 situation.
- Pay attention to who is fed on which team. If your team is behind realize you don't want to team fight and try and look for picks. Only engage if you know only 1 or 2 enemy players are there. If team ahead, try and pick fights but don't do it 1v5 make sure your team is with you.
- Ward major objectives such as dragon or baron. Pay attention to enemy team moving on map to see if they trying to sneak a baron.
- If your team wins a fight look to take an objective. Most likely this means pushing mid or another lane. Make sure to retreat when the enemy team re spawns. Too many players especially in silver & bronze overstay in enemy base, which leads to throws.
- Really just repeating most of the above all game while making sure to not get caught alone by enemy team especially in lane game. If you catch an enemy out late game so its 4v5 try and force a fight as your team has a huge advantage. If your team secure the ace or kills 4/5th of enemy team you will most likely be able to end.
- DON'T CHASE KILLS. There is securing kills and then there is blindly chasing a kill all over the map forever. Stop doing the chasing around the map forever kills as it generally = wasted time or leads to being baited to your death.
There's a lot to this game but once you learn more and become more confident ranking up becomes easier until you meet players who know the game on an equal level with you. Then you have to learn more before you can continue to beat those players more than they beat you. The cycle continues until you reach your goal rank or stop improving.
jungle. Roughly 2 seasons ago I looked up a j4 guide and my mind was blown on how to gank as 
