Q1. IS it possible a flow of electricity without an electric field?
If you mean is it possible to have flow of electricity that's not caused by an electric field, consider Millikan's oil drop experiment, before the external electric field is applied. Ions attached to drops of oil flow downward due to gravity acting on the oil drops. That's a (very tiny) current caused by gravity rather than by an electric field.
But there were of course electric fields present during the experiment since each ion produces a field of its own.
Q2. I've learn that moving of particle with electric charge in electric field makes potential difference.
That doesn't sound right. Read my answer to another recent question for a clarification about why the potential difference is present even when there's no mobile charge present for the electric field to act on.
Then, let's suppose no resistance in wire. IF Q1 is true, wire with a flow of electricity makes an electric field, and in the electric field, an electron moves. Then potential difference must exist. But when measured, there is no potential difference.
The solution to this is to realize that (leaving aside superconductivity) no wire with 0 resistance actually exists. So every real wire has at least a small resistance, and if there's a current in the wire, then a small electric field must be present there to make that current flow.
We should only make the ideal wire approximation when the resistances in the wires of a circuit are much less than the resistances of other elements in the circuit, so that considering the wire resistance would complicate understanding of the circuit behavior without changing that behavior appreciably.