(on a weekend, 5 in the morning in Belgium!)
I'm in Canada, not Belgium (though it is after 5am here now; I got up and had to check the forum/email on my way back to bed...
). I work evenings and weekends, since that is when more people play games (and working late I can overlap with the morning in Belgium).
Not all items have a handle, only global items. Picking a local item up and dropping it will create a handle for it.
Deleting a handle does not allow it to be reused.
I don't know about the removed items. I can ask about that, if it matters in light of the previous answer.
The handle generator uses two parts, one of which is a global counter (which only increments each time it is called), and doesn't keep track of or look for handles that are no longer used.
I don't know about ItemHandleMoveTo.
AFAIK local items don't use a handle.
I was told this could not be fixed for D:OS, but that would be changed for D:OS 2. I don't know if that was purely for technical reasons, or the chance of major changes breaking things for others was too great a risk given the relative rarity of issue with the higher limit.