Don't know what the mirror thing is, but I should I've seen one before.
The Dalmeyer Pantent Portrait lens dates I think from 1866. You can maybe find something here. I have a Wray lens of maybe the same rough vintage, same focal length, the elements unscrew, easy to clean with care. I use glass cleaning fluid and it restored a Dagor that I was assured had separation, it had 70 years of accumulated grime that was all
Try careful cleaning
My guess is probably right that you're camera is Whole-plate at the most, my own early 12" rectilinear lens is designated for 8"x5" (with movements), but yours is a Portrait lens so a touch longer than a standard lens.
I have some old books 1880's with Dallmeyer equipment in but they are in storage back in the UK or I'd scan and send you what I have.