Slit screen and wave-particle duality

The answer is yes to both questions: yes, the screen does show one location for one particle and yes, the accumulated picture after repeating the experiment many, many times does show the interference pattern.

There is a set of beautiful pictures and a video of the double slit experiment in one-particle-per-time mode that can be found here (the experiment is with electron but conceptually there is no difference).

Let me try a slightly different way to answer this (well worn) question.

The photon doesn't have a location, or at least not a well defined location, until you interact with it and cause it to localise.

When the photon hits the photomultiplier, or photographic plate, or whatever you're using as the screen the interaction occurs at a point and that localises the photon. Until then it's somewhat meaningless to talk about the position of the photon. I don't mean the photon has a position but we don't know it, I mean the photon simply doesn't have a position. That's why it doesn't make sense to ask which slit the photon went through. because the photon's position is ill defined it occupies the whole experimental apparatus.

So a single photon does indeed passthrough both slits, but it then interacts with the screen at a point. The point of interaction with the screen is random, with the probability o the position being given by the square of the wavefunction. That's why over time the pattern created by many phtons gives you the interference pattern.