Yes, the slots are for cleaning ash from grate. Insert slicer knife through slots, flat across grate and with a slicing motion work back and forth and side to side across grate. This drops ash through grate easily. The doors prevent air from leaking in making the stove burn harder.
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Slicer knives slowly wear out. They get smaller looking like an envelope opener as they wear away. A flat bar works, but should be ground with an edge on the sides to move under coal easily. The in and out motion drags some ash out of the slots, so a sideways motion as well is cleaner for the home. Practice makes perfect.
The plate across the front is called a banking plate for coal, and a wood fence for wood. Normally they are solid for coal, straight across the top like a dam. Yours looks like one for wood, but maybe that stove uses the same one for both, it appears it may be set up for wood, and your missing the coal banking plate. After coal fire is established, this is the height you pour coal on fire up to. It prevents coal from falling toward door to hold the level over grate.
Putting coal in is called stoking the stove. If it had a large funnel shaped ring at the top, that would be a hopper. It looks like a barrel looking into the top of stove. Oval shaped like a big cone over the fire. Coal is poured through the top and filled to the top of stove. It only burns under the hopper on grate and around hopper. As it burns coal, gravity allows the coal supply to fall onto grate. As you clean fire, coal slowly drops making its way onto the grate. Not all coal stoves are hopper fed, some are stoked, or loaded by hand.
The hopper is normally adjustable in height. They set or hang on ridges that you set the height above grate. The lower the setting, the lower the coal under and around it. Raising the hopper allows the coal to be deeper under is, falling around the sides for a thicker hotter fire. Removal of hopper converts to wood use. This is called a combination wood/ coal stove.
This is why I’m unsure what you have, looks like a combo in the wood mode, but can’t see the inside well enough to tell.
The thermostat controls primary air under grate, up through coal bed. The control on the right upper corner opens a door that lets air into ash pan area under grate. American Stoves use a bimetallic spring to open door as it cools to maintain the set temperature. As the stove heats the coil, it closes the door to slow air flow slowing the fire.
European Stoves use light oil in a closed tubing system called a capillary tube. Like the sensor in an older gas oven, the fluid expands and contracts with heat using hydraulic action to open and close a door flap to adjust how much air is allowed into ash pan area. One end of capillary tube is closed off like a swelled up end in the tube full of fluid. This is placed in cool air flow moving toward stove to sense ambient air temp. The other end acts on a diaphragm to move door. You can probably see it easiest removing ash pan, and by turning up the control on back it should open, or since the stove is cold it may seal open waiting for heat to close it. Do not move the flapper door by hand. This type is much more accurate than a bimetallic spring type.
You “ can” burn wood in any coal stove. Just not efficiently. It will burn fast since it gets so much air, and coals fall through grate not allowing them to build up prolonging the fire. Stoves are designed for one fuel or the other. Combination stoves will operate better on one fuel or the other. This design is primarily a coal stove. Best for coal. Wood stoves converted for coal do much better with wood.
These are very efficient, normally burn pea size coal, that goes by what size does not fall through grate.
This is a very basic crash course on how these stove work. Don’t want to confuse you with the details on each part and tips you learn with use. You will have questions firing it, and there is a learning curve learning coal, but so much easier than wood with a steady heat output until you leave it go out in the spring!