If you have std wheels then unless you have coilovers, the wheels are that close, the spring platform is very close and I could not get my little finger between tyre and spring platform either, it's normal.
As for pulling to the left, there is no reason why it or any cossie should do it.
BUT certain things will make it do it, such as low tyre pressure that side, worn bushes, bent tca, check wheelbase between centre of front and rear wheel each side, they should be pretty similar.
Even repairs in the road can induce pulling and some tyres are very sensitive to this, my F1 were but thank god they are gone now.
Make sure the road is flat, the best way to see if it is really pulling one way is to drive in the centre of a decent road and see if it tracks straight and true..
tabetha