Unless you're using a special multi-layer material with a top layer that has real thickness, set the engraving depth to zero.
Are you using a V-shaped bit, and did you tell Halftoner what angle the bit is? If you're using a 90 degree bit and telling Halftoner it's a 60 degree, for example, it will plunge much deeper than it should.
Halftoner assumes that the zero is the surface of your material, so if you're setting zero lower than the material surface that could also be a problem.
Spacing should be slightly larger than the maximum hole size, unless you're using the "Offset odd rows" option with dots mode, and then you can use a spacing that's just slightly smaller than the max hole size.
Take a picture of the bit you're using (or just post the specs for it) and screen shot the panes for settings and toolpath and post them here. The results you're getting are quite odd, for sure.