in an assembly, how can I randomly place identical parts into a container to fill it?

I can't think of an accurate method largely due to the difference between the head/body diameters of the screw. The safer bet may be to base the fill quantity on the volume of space taken per screw (head diameter X overall lgth) divided into the volume of the container. This will likely result in a safety factor because the screws will nest in smaller spaces if they "interlock" with each other. That safety factor would result in a given number of screws fitting into a container with some room to spare. This is better than underestimating the space and not packing the correct number of screws per container.

Use SW Motion.  Create a table with a funnel end sloping into bucket, add a screw and rectangular pattern it on the table, insert gravity, lock table and bucket, run sim.  Be prepared for this to take a while and lots of fiddling with settings.  Oh! and you will have to set up global contact. Simplify your screws as much as possible.

I might even try this myself as an academic exercise:)