When you drop a weapon on the ground and tell your zombie to use it, he doesn't do anything.
I was testing this with an old PC. It does work, sort of, but it's iffy. I found it only worked when I dropped a weapon at my feet, walked off to the side to let the zombie have a clear line to get to it, then told it "use this weapon". And, it wouldn't ever equip the last weapon I gave it, but whatever it had picked up just before that one.
it needs an enemy to engage to equip it after it picks up the weapon
I never got it to pick the weapon up off the ground.
Most likely, the summon needs to be fairly close to the item.
Your best bet would be to use the Player Tool to direct your minion to walk as close as possible to the item. If you set them to Stand Your Ground, they will walk to the point and stay there.
Then, just speak to them as normal and try again.
Let us know if that doesn't work, however.
We had a slight hiccup in the module and the content was removed after being initially implemented. It is confirmed to be working now correctly.