Focusing on positioning and farm will drastically improve your gameplay. I noticed you have a tendency to over extend, especially around turrets. If you are going to go in you must have a way to get out. Your A is one of the best ways to do this especially if your going to dive turret for a kill. In order to do this effectively you must:

A. have your ult to dive in (in front of your target) and use your A to dodge turret fire + gtfo
B. already be strafing in front of the hero you are chasing using your heroic perk and then use your A to dodge a turret hit on your way out.

If you cant do any of these, weigh your losses and keep your life. Below level 6 it is really hard to pull off a turret dive as there is no way out.

The second thing is farm. You need to be on constant rotations sweeping through you jungle. Buying the War Banner was the right choice because it allows you to clear camps faster but you never used it. From minute 3 to 7 you never killed a creep, staying at a CS of 9 for four minutes. It may look like your team needs you in lane but getting more items early is going to benefit your team in the long run.

What i'd like to see you focus on is placing vision around the center of the map and paying attention to when all three enemy heroes are in the lane. Use this time to steal camps from the enemy jungler while placing vision so you can figure out where they are and when the time is right to sneak in a steal farm. If you take one thing away from this it should be to stay on a farming rotation and to check the lane only while you are waiting for camps or an essential turret is going to be taken.