Yes, both are directly proportional to each other. When traffic will come then ranking will increase by-default.
Yes, traffic most certainly does affect your page rank.
It is important to have traffic in order to increase your rankings
Once visitors are on your site, it is also important for them to engage with it, this too helps with site rankings. It's much better for a visitor to land on your site and use it than to "bounce" right off.
Yes, Traffic impacts on ranking. It means more traffic has more ranking.
We can't say properly that traffic impacts ranking. For ranking, organic traffic is most important. A website rank well if we make quality links either it is do follow or no follow. At some point it impacts the ranking.