How does the current flow in the short circuit wire ? Isn't potential difference necessary for existence of current?
Try looking at it the other way.
Ask yourself what would happen if current didn't flow in the short-circuit.
The answer is that the potential difference across it would rise. If the PD rises then current will flow.
The circuit settles down with current flowing. All the rest of the wiring in the current loop is a short-circuit too.
I don't know enough about cooper-pairs (which form up two electron fermions into a boson particle) to answer your question with respect to super-conduction. You may have to ask a specialist physicist that question, if you are interested in it. (I did find this discussion, though: How does current flow in superconductors.)
However, electrons as fermions are accelerated by a very small charge gradient that appears only at the cylindrical surface of the (copper, say) wire. This gradient sets itself up quite quickly and forms the accelerating forces required to move charges. If you place a bend in a wire, there will be yet another slight accumulation of charges at the corner of the bend at just the right level required to divert the electrons around the bend.
(Note that a copper wire does possess a small resistivity so there will be a slight potential difference, one end to the other.)
There are some good physics books that discuss exactly how this sets up and happens. I'd recommend the most recent edition of the one called "Matter & Interactions." (I have the 3rd edition here.) See this Matter & Interactions video on Surface Charge with respect to what I'm discussing here.
Isn't potential difference necessary for existence of current?
No. A potential difference is required for a current to flow through a resistor. An ideal conductor can sustain current without any voltage applied to it.