Well first regarding the points of the brexiteers, these are quotes which have been taken terribly out of contest, for example with the 350M quote from Farage, he said it was a mistake to suggest that money would all be spent on the NHS, because the reality is the government will have the control of that money, which wasn't the case before, so the government can choose to spend that money on the NHS, or on schools, roads, bridges, etc. Not necessarily on the NHS, although if the elected government wanted to spend all 350M on the NHS, they could. The whole point of Brexit was to take back control.
I am well aware that both left and right wing media have a bias, that's expected. However, the left's new trend is a constant pursuit of obfuscating reality, which is very different, like the example I gave on the Nice attacks, or how major left-wing papers have simply chosen to ignore the worrying increase of rapes in Germany, etc. Right wing media may be partisan, but at least they aren't trying to hide reality. Also it is impossible to escape left wing media, the BBC here is not as shameless as the CBC but they give it a pretty good try, and I usually read lefty posts to engage with different opinions, that being said, when I actually want to find out what's going on in the world, I am better off reading a proper newspaper.