The full add-on: Drop to Bed with all Move, Centre and Origin options, Lay Flat, both zips (Blender extension and legacy add-on), the documentation and free updates for 1.x. It is licensed GPL-3.0-or-later, with no account, no trial and no nag screens.

With the built-in tools you find the lowest point yourself, type or snap the Z value, and do it again for every object; Set Origin has no 'bottom centre' option. Drop to Bed measures the final shape in world space (rotation, scale, parents and modifiers included), puts its lowest point exactly on Z = 0, and can centre the model and set the origin in the same click, for many objects at once.

Drop to Bed and Lay Flat only move and rotate the object. Only the Origin: Bottom centre option shifts the mesh data, and it moves the object by the same amount, so nothing changes in the world. It never cuts, remeshes or repairs.

No. You choose the face that goes on the bed and Lay Flat makes it exact. Finding an orientation with fewer supports is a different job that this add-on does not do.

Blender's default scene counts 1 unit as 1 metre, and STL files have no units. Set 1 Blender unit = to 1 mm in the panel (or set Scene > Units > Unit Scale to 0.001). The drop to Z = 0 itself is the same in any unit.

The face points straight down, but another part of the model reaches lower (for example a peg or handle), so the object rests on that part. The report says how many mm the face is above the bed. Pick a face on the outside of the model, or cut the part away first.