My last name is Parkhomchuk and for short it’s Park does that mean that Parkhomchuk originated out of the Korean Surname Park?

"Leigh", sometimes spelt "Lee", is a popular surname in Britain. "Kim" is a popular given name in Scandinavia, especially Denmark. Neither "Lee" nor "Kim" derives from the Korean "Lee" or "Kim." They originated independently. There are hundreds of names that bear striking similarities to one another, that doesn't mean that they're connected or that they share a common root. There are thousands of Germans with the surname "Kahn" which has absolutely nothing to do with the Asian surname "Khan." Plenty of people in Western countries have the surname "May" which is pronounced in exactly the same manner as the surname "Mei" in Asia, and again, that is due strictly to coincidence.

Keep in mind that the Korean surname 이 is actually pronounced closer to "ee" (no "L" / "R" sound - it can be rendered "Lee", "Li", "Rhee", "Ri", etc.), the surname 김 is actually pronounced with a soft "K" sound, almost a cross between a "G" and a "K", and the surname 박 is actually pronounced something closer to "Bahk" than "Park", it's only pronounced "Park" when it's Anglicised.

So no, your surname and the Korean surname are not similar, they have zero connection.