The number of photoelectrons emitted from metal surface will depend on the energy of light wave incident on metal surface. Now let the maximum no. Of electrons that can be emitted by the given light wave be 'x' or let this be an integer for e.g. 100 electrons are emitted, now only these 100 electrons are responsible for carrying current.
Now, the main point comes further, so read carefully.
the maximum kinetic energy of electron be k°
not all the ejected electrons will be able to reach the other plate, this is because few electrons will suffer collision with other electrons or will suffer collision with the gas molecules(basically inert gas atmosphere is taken, for which inert gases like helium or argon is taken).
Due to collision few electrons will not be able to reach the other plate. And for few electrons, the minimum K.E. required to reach the other plate will be less than what is required.
let 60 electrons dont reach the other plate.
Now we apply potential difference in the circuit so that electrons now have ease to reach the other plate efficiently.
Let 10V be the pot. Diff. Applied, now let 10more electrons reach the other plate in the fluence of the pot. Diff.
Further increasing the pot. Difference to 20V let 10 more electrons reach the other plate, now remaining electrons is 40
Now in this way increasing the por diff. So that all the 100 electrons are able to reach the other plate, now, the remaining electrons which are unable to reach other plate would be zero. As all the electrons are now able to reach the other plate, now the current which is directly proportional to applied potential reaches its maximum value and after reaching this maximum value, on further increasing the potential difference, current should have also increased(hypothetically) but the fact is that number of photoelectrons reaching the other plate is now 100, which means all the ejected photoelectrons are now able to reach the other plate. On further increasing pot. Diff. Would not increase the no. Of photoelectrons that reach the other plate(i.e. the carriers of the current) the no. Of photoelectrons reaching will now be 100 only, and will not increase beacuse of increase in pot. Diff thus current after reaching its saturation value cannot be further increased.
Regarding the second point,
The current flowing depends on the intensity of light. The electrons flow in the area between the plates in almost same speed as in the wire.