Doors – My apartment door unlocked by itself. Can anyone offer an explanation please

On numerous occasions I have had to cut hollow core doors off more than the available blocking in the top / bottom of the door. What I have done in these instances is to take the cut off bottom piece and then reclaimed the inner block for re-use. If a table saw is available it is quick work to set the fence just right so that a couple of rip direction passes cleanly cuts off the outer laminations. Alternatively the laminations can be removed using a plane.

Once the block is nicely cleaned up it can be glued and slipped right up into the open bottom of the door. Use a couple of 1x4 boards on either side of the door and some good sized C-Clamps to tighten up the glue joint so that the glue can dry without any gaps.

Note that often the inside of hollow core doors has an internal webbing of cardboard material to bridge the gap between the two lamination skins of the door. Sometimes it is necessary to use a chisel inside the cut open bottom of the door to scrape back the glue joint of this web material on the laminated panel. If this is not smoothed out the re-claimed bottom block will make the laminated sides bulge out when trying to glue the block in place.

My guess is that the removal of the set screw (which you called the grub screw) will allow the post piece of the door knob to be removed from the door. A good pull may be required to remove it.

You should look at the door handle on the opposite side to see if it also has a similar set screw. If it does not have any visible means of removal then the knob from the opposite side will pull from the door extracting a central shaft which is extending into the post that you see on this side. The set screw in this case is holding the handles in place from both sides.

Once you get the post off the near side reattaching your knob lever should be as easy as accessing the head of the central screw from the inside of the post piece. The central screw head may use a normal screw driver or may be a six sided hex similar to the set screw head.