First, Don't run it with the door open!! You will let CO into the room. Do you have a CO detector?? If not, get one.
Many stove do not have any internal plates or anything, they are just open as shown in your pictures.
Looks like it is working properly. The Brick may control some type of stove draft internally, it looks like it is part of the exhaust system. Maybe there is hole behind and you can adjust the opening for less draft on the bottom of the stove and it may pull some from the top? Not sure, I would leave it alone for now.
You may have to adjust your feed rate a bit and get a slightly bigger burn area to get more heat out of the stove. You should have 1/2-1" ash at the end without it pushing hot coals over the end to get max. heat out of the stove. maybe get a magnetic thermometer to measure the side temps and see what they are?
Do you have a blower to move heat into the room? Do you have a thermostat or rehostats to control the heat?
The DV or PV (direct/power vent) and Baro Damper (if you have one, if not, you should) so, you can adjust the draft on the stove to a proper setting (.02-.04). Without a Baro damper, you are wasing fuel and sending more hot air out your chimney.