Why is it more difficult to remove an electron from Fluorine or Helium than it is
to remove an electron from potassium or
Cesium?

In general, the further away an electron is from the nucleus, the easier it is for it to be expelled. In other words, ionization energy is a function of atomic radius; the larger the radius, the smaller the amount of energy required to remove the electron from the outer most orbital. For example, it would be far easier to take electrons away from the larger element of Ca (Calcium) than it would be from one where the electrons are held tighter to the nucleus, like Cl (Chlorine). Hope this helped a little not the exact answer though :)