Why is the current flow shown to be flowing from the negative area towards the positive area?
By convention, positive current is assumed to be the direction of flow of positive charges. The trouble is that in many common situations (like this one), the current is actually carried by electrons which are negatively charged.
It can be confusing. Blame it on Benjamin Franklin. The convention for current flow was based on his work, before anyone knew about electrons, protons, and ions.