When, like now, can I cut it back and how far back? Some of it's about 20"
tall, but I would like it to be lower.

The natural height of Mahonia aquifolia, Oregon grape holly, is about 4 feet.
If you want something under 20", plant a different species. You may kill it
trying to keep it cut back that low. There is a Mahonia repens native to the
eastern part of the country which is much lower growing, but not as attractive.
I don't think it is in the trade. You would have to go out in the woods &
collect it. If you want a ground cover, you can't go wrong with Pachysandra.

the growth that keeps coming to enable the plant to spread in the area it
covers, can I clip off this growth and hit it with Brush-B-Gon or will this
damage the plant?

Weed killer will spread and kill the plant. If you have to fight with it that
much, plant something else. Put your Oregon grape out in the yard somewhere
with more room. Enjoy the yellow flowers when the Rhododendrons bloom, & let
the birds enjoy the berries. Incidentally, Mahonia belongs to the barberry
family, but I have never heard of it being implicated in white pine blister
rust.

Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)